Is it bad to apply for a second postdoc immediately after starting a first one? I have finished my PhD in pure mathematics 3 months ago, and have just (one week ago) started a 1 year post doc appointment in another area of applied mathematics (it has only very very minor links with my PhD, and I really don't know how it will turn out - but I am not very into it so far). 

I have had this offer for a few months, and took it because my other post doc applications in areas more closely related to my original topic were rejected; I was on the shortlist many times, but ended up 2nd in the final choice. 

Now I have yet another opportunity to apply for a post doc in a topic that is close to my PhD, back in my home country, with people who are world-leading experts in my field, at a world leading, prestigious department and university (my current one isn't). Another advantage is that my current post doc only has guaranteed funding for 1 year, while the one I want to apply for, has 2 years.

This post doc has a provisional starting date in 2 months time. This means I'd have only worked in my current position also for only 2 months.

In my situation, is it advisable on the application form to state that I have currently just started on a post doc, or say absolutely nothing at all (i.e. not even mention this on my CV)? 

I am worried that it won't look good on my application that I am applying for new jobs after having barely started the first one.
(This answer assumed the OP was going to be job hunting after a few months for a new position following his current one.  Clarifications given in the comments shows the OP expects to leave the current one-year position after a few months, instead.)

If your first position is only a year long, then it is expected that you will already be searching for a new position before you've even arrived at the current one.  There's simply no choice: most committees are already forming short lists a month or two into the academic year.  This is what makes one year positions brutal: as soon as you get one you've got to start hunting for the next one, but your current post-doc position still expects to see you engaged and active in research and whatever teaching you may have.