I have started writing my thesis ( just yesterday:) ). My advisor asked me to submit it in one or two months. Now am wondering should I start applying for jobs at this time period. I plan to talk about this with my advisor. But I thought of other opinions as well. Please share your experience also.
Yes, you should start applying for jobs. You should have started several months ago, since it can take time to find a job, and after you do it may still take some months before the job actually starts. This depends strongly on what kind of job it is.
Of course, if you are looking for an academic job in the US, the interviewing season is roughly November-March, so you want to time things around that. For industry jobs and academic jobs elsewhere, there is not usually a particular season to focus on.
I agree with @DavidKetcheson. You should be able to get some sense of the "lead time" on jobs of the sort you're interested in by browsing current adverts: what is the typical "start date"? For competitive academic positions, this might be as much as a year ahead.
However, there may be strategic reasons to delay, accepting the risk that you can't start working (and earning money!) as early as you wish. For example, you might feel you're likely to be able to secure a much better job if you publish a particular piece of work before going on the job market. There's also the issue that job-hunting can be a time-consuming business: plenty of people decide that they'd prefer to concentrate on completing their thesis first, and then focus on finding a job. I don't think this is an a priori unreasonable approach to take, particularly if you're in a system where there is some significant amount of "dead time" between submitting your thesis, and having the defence.
Regardless of the approach you take, you should certainly be looking at job adverts now, to get a sense of what might be available, and what people are offering/looking for.