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‎In this paper‎, ‎we introduce and investigate an interesting subclass‎ ‎${\cal{S}}^{h,p}_{\Sigma}(A,B,C,\lambda)$ of bi-univalent functions in the open unit disk $\mathbb{U}$‎. ‎Furthermore‎, ‎we find estimates on the $|a_2|$ and $|a_3|$‎ ‎coefficients for functions in this subclass‎. ‎The coefficient bounds presented here generalize some recent works of several earlier authors‎.