  In this paper we prove that the $p$-adic $L$-function that interpolates the
Rankin-Selberg product of a general weight two modular form which is unramified
and non-ordinary at $p$, and an ordinary CM form of higher weight contains the
characteristic ideal of the corresponding Selmer group. This is one
divisibility of the Iwasawa-Greenberg main conjecture for the $p$-adic
$L$-function. This generalizes an earlier work of the author to the
non-ordinary case. The result of this paper plays a crucial role in the proof
of Iwasawa main conjecture and refined Birch-Swinnerton-Dyer formula for
supersingular elliptic curves.
