Abstract.</strong> In this paper, we consider a general subclass $H_{\Sigma}^{\lambda}(h,\beta)$ of bi-univalent functions. Bounds on the first two coefficients $|a_{2}|$ and $|a_{3}|$ for functions in $H_{\Sigma}^{\lambda}(h,\beta)$ are given. The main results generalize and improve a recent one obtained by Srivastava [18].