  We study the partition function of the ABJ theory, which is the N=6
superconformal Chern-Simons matter theory with gauge group U(N)xU(N+M) and
Chern-Simons levels (k,-k). We exactly compute the ABJ partition function on a
three sphere for various k, M and N via the Fermi gas approach. By using these
exact data, we show that the ABJ partition function is completely determined by
the refined topological string on local P^1 x P^1, including membrane instanton
effects in the M-theory dual.
