Let $G=(V,E)$, $V=\left\{ v_{1},v_{2},\ldots ,v_{n}\right\}$, be a simple graph of order $n$ and size $m$. Denote by $\Delta = d_1\ge d_2 \ge \cdots \ge d_n= \delta$, $d_i=d(v_i)$, and $\Delta_e=d(e_1)\ge d(e_2)\ge \cdots \ge d(e_m)=\delta_e$, sequences of vertex and edge degrees, respectively. If vertices $v_i$ and $v_j$ are adjacent in $G$, we write $i\sim j$. The modified second Zagreb index is defined as $M_2^*(G)=\sum_{i\sim j} \frac{1}{d_id_j}$. In this paper we determine some new upper and lower bounds on $M_2^*(G)$ for a line graph L(G) of G.