I gave a manuscript to my advisor while ago but he doesn't read it, what is the best action to do cause I need to publish it fast?
If talking to your advisor doesn't work, I would suggest emailing your advisor with the draft, saying that you plan to submit it to XXX on such-and-such a date and that you would be grateful for any feedback he or she can provide you before then.
As mentioned by amirg, you might also run it by the head of your lab, if that's the standard in your field. (It's not in mine: computer science.)
Since, you are near your graduation, that means not only you know whether your research results are publishable or not but where to publish those results as well. Consequently, similar to what Suresh suggests, one of your problems is not only to publish those results but publishing them on a suitable venue which is a) close to your area of interest b) it is a high-profile journal of conference c) your paper has a lot of chances to be actually accepted. So, it is part of your job to actually find such a venue to stress the urgency of your publishing those results.
In this sense, have you checked the nearby CFPs (call for proposals) for related conferences or journals? Perhaps your advisor plans to submit your paper to an event which is 2-3 months from now and is already confident enough for your draft, so there is no immediate hurry to do the final changes now. Many advisors are very busy and allocation for their various tasks is done according to their deadlines, so perhaps this is the reason he has postponed providing feedback. If you have found an alternative venue for publishing those results with a closer deadline, it will be easier for you to convince him to check your manuscript ASAP.
But in the end, we are just random Internet strangers and the most proper solution is (as others have suggested) to TALK TO YOUR ADVISOR.
Original Answer: If you are submitting to a journal, you do not have to have your advisor's approval (unless you are using his dataset or it is coming out of his lab). If it is based on your own research findings, publish it as single-author.
Editorial Note: You did not indicate your discipline. As state in the original response, this answer is only applicable for disciplines where your research is independent of your advisor's research, lab, or research grants.