We generalize the Pollack-Rubin proof of the Iwasawa main conjecture for CM elliptic curves over Q at supersingular primes to CM elliptic curves over an abelian extension of the imaginary quadratic field given by CM. We will explain the precise set-up, how to construct plus/minus algebraic p-adic L-functions and plus/minus analytic p-adic L-functions and how they coincide. This is a joint work with Byoung Du Kim and Bei Zhang.