Which part of physical B model is not rigorous? the physical theory of B model,if it is not mathematical rigorous just because the Feynman integral,but it looks like for me the space is finite dimensional, what the problem is causing that it still not rigorous?

To define (as Kevin Lin does above) the Bmodel purely as the derived category of coherent sheaves is fine and rigorous, but it ignores the highergenus aspects of mirror symmetry  which was the original question. As I wrote above, Kevin Costello gives a rigorous description of the highergenus amplitudes, but it is still conjectural whether this agrees with the physics. The issue is that highergenus string amplitudes depend on an integration over the moduli space of Riemann surfaces (or a space of maps from them, depending on the model), and this demands compactification. The full, nontopological theory is of course an ordinary twodimensional quantum field theory, with all the usual difficulties in making the path integral rigorous. 


Kevin Costello's mathematical definition of the Bmodel (math/0509264) is rigorous. It's an open problem whether this definition agrees with the BCOV construction, as far as I know. 


Openstring Bmodel seems to be ok: derived category of coherent sheaves in the CalabiYau case, matrix factorizations in the LandauGinzburg case. The following are closedstring Bmodel, but genus 0 only:
For the higher genus closedstring Bmodel, see this question. 

