I have started my 1 year postdoc in math three months ago, of course after 1 month the university was closed and I have to work at home, due to Corona Virus. Recently, I want to apply for another postdoc position in another country. One of the required documents is a letter of recommendation from current mentor. I do not know whether it is reasonable to ask a recommendation letter from my current mentor, because I have just worked with him for a short time. Does he give me a recommendation letter?
One-year postdocs are weird. At least in the US (I guess you may not be based on the timing of this question), if you are looking for another academic job, then your next round of job applications might be due sometime between 2-5 months after you start your postdoc, and you probably want to ask for letters at least 1 month before the first due dates. This means, global pandemic or not, your postdoc mentor can only get to know you so well before it's time to ask for a letter. (And just because there's a global pandemic, doesn't mean you can maintain communication with your mentor.)
My advice is: ask for letters from people who can best evaluate your work, for the kinds of jobs you're applying for. So the answer to your question depends a lot on your situation and your relationship with your current mentor.
For research letters for academic jobs, you should ask a selection of people who can give a good overall picture of your research spectrum to date (maybe you've only worked in one focused area, but maybe you've worked on several different things, and you don't want to end up asking only people who can talk about aspect X of your research and all ignore aspect Y). I assume you are still young, rather than having postdoc-ed for 10 year now---once you've been out awhile and have a larger body of work, you want to focus on your most important and your recent work.
That said, there are a couple rules of thumb to balance against this:
It's standard to ask your PhD advisor for a letter, at least if you're a recent PhD. If you've done multiple years of postdocs, it's also common to have at least 1 letter from a postdoc mentor, but it also doesn't look weird to not have one because postdoc mentors may or may not know your research better than senior collaborators, experts elsewhere, etc. The point is that you don't need to ask a postdoc mentor to write you a letter just because they are your postdoc mentor.
It looks better if your letters come from both a variety of institutions and well-known experts in your field, to show that your work is well regarded by (at least a small part of) the community. So if all of your other letters would be coming from your PhD institution, then I would definitely try asking your postdoc mentor (or think of some other experts, who you may or may not know personally, but are familiar with your work--e.g., maybe they've cited your papers or asked questions at a talk you gave). As long as you have a decent relationship, and your mentor is familiar with some of your work, I would expect your mentor to be willing to write a letter.