Let $p$ be an odd prime, $f$ be a $p$-ordinary newform of weight $k$ and $h$ be a normalized cuspidal $p$-ordinary Hecke eigenform of weight $\ell < k$. Let $p$ be an Eisenstein prime for $h$ i.e. the residual Galois representation of $h$ at $p$ is reducible. In this talk, we show that the $p$-adic $L$-function and the characteristic ideal of the $p^{\infty}$-Selmer group of the Rankin-Selberg convolution of $f$, $h$ generate the same ideal modulo $p$ in the Iwasawa algebra i.e. the Rankin-Selberg Iwasawa main conjecture for $f \otimes h$ holds modulo $p$. This is a joint work with Somnath Jha and Sudhanshu Shekhar.