  In this paper we prove that the p-adic L-function that interpolates the
Rankin-Selberg product of a general modular form and a CM form of higher weight
divides the characteristic ideal of the corresponding Selmer group. This is one
divisibility of the Iwasawa main conjecture for the p-adic L-function. We prove
this conjecture using the congruences between Klingen Eisensteinseries and cusp
forms on the group GU(3; 1), following the strategy of a recent work of C.
Skinner and E. Urban. This theorem can be used to deduce a converse of
Gross-Zagier-Kolyvagin theorem and the precise BSD formula in the rank one
case.
