As I'm not native speaker and I aim to improve my academic English (spoken and written) i'm asking if reading newpapers is good way to improve academic English? Or they don't use academic English in their context?
Reading newspapers has some value, but it should not be your only effort.
Read English translations of literature and biographies that you know well. Listen to audio recordings of these works. This will allow you to concentrate on the language rather than the content. It will expand your regular vocabulary and improve your grammar. Write your own short stories from scratch to practice your regular English vocabulary and grammar.
Read academic papers written by native English speakers who are also well-known in your field. Translate your native language lecture notes and papers to English to practice your written academic English. This exercise will allow you to concentrate on the language without worrying about the validity of the content.
Engage as many native English speakers in conversation as is practical. If you have colleagues who are also proficient in English, then engage them in conversation and ask for their feedback on your written academic English.
In your title question you ask about academic vocabulary but in your main text you ask about academic English. These are different. Also, there is a difference between reading and writing (and also between listening and speaking). So:
For vocabulary, unless your academic field is one that is covered by newspapers (e.g. politics) then I don't think newspapers (even serious ones such as the New York Times or the Times (London) will be any help. Even if it is one of those fields they will be of very limited use. Those newspapers are intended for educated lay people. They will not use technical vocabulary unless it is absolutely necessary.
For understanding written English, serious newspapers may be of some help, depending on your current level of English. Unfortunately, academic English in many fields has a tendency to be rather turgid and not as clear as newspapers. There are several reasons for this.
- Most academics are not trained in writing; all journalists should be.
- Many academics are not native English speakers. It is hard to write clearly in your second (or third, or fourth) language. Some manage it, but it's hard.
- Academic journals generally do not highly value clarity.
Still, if your current English reading level isn't very good, then reading well written newspapers could help, but so could reading well written books.
As for writing, speaking, and listening, I think that reading can be of some use, but the best way to learn anything is to practice doing that thing.
In terms of written English, newspapers are of limited help, because most academic fields have rather stringent requirements on how written communication (mainly journal or conference articles) are structured, and newspapers do not follow these conventions. This especially applies to STEM fields, like the "Introduction-Literature Overview-Methods-Results-Discussion" structure in experimental papers. The vocabulary is also often highly specialized, and limited compared to standard English. It may be better to simply read papers in your field.
In terms of spoken English, newspapers may be more useful. After all, it's quite as important to be able to talk to people at conferences, or in videoconferences during collaborations, and here some "normal" English is helpful. In this direction, you can actually use pretty all the "standard" methods of improving your English: watch movies in the original, listen to podcasts (either one can easily be done while working out, perhaps while doing chores), or simply read English books.
It is not good for learning technical vocabulary. But it is good for improving your English in general and learning how to express ideas clearly. Newspapers almost always explain ideas very clearly, whereas academic papers are sometimes unnecessarily hard to read.
("Unnecessarily hard to read" means some academic papers are hard to read and this is not just due to the technical or academic nature of the content. They could have been more easy to read, if the authors were better at writing.)
As Dimitri Vulis suggested, you should read serious newspapers and not tabloids.