Let $M_g$ be the moduli space of hyperbolic surfaces genus $g$ endowed with Weil-Petersson metric. In this paper, we show that for any $\epsilon>0$, as goes to infinity, a generic surface $X\in M_g$ satisfies first eigenvalue $\lambda_1(X)>\frac{3}{16}-\epsilon$. As an application, also diameter $\mathrm{diam}(X)<(4+\epsilon)\ln(g)$ large genus.