In this paper, we introduce and investigate an interesting subclass N-Sigma(h,p) (lambda, mu) of analytic and bi-univalent functions in the open unit disk U. For functions belonging to the class N-Sigma(h,p) (lambda, mu), we obtain estimates on the first two Taylor-Maclaurin coefficients |a(2)| and |a(3)|. The results presented in this paper would generalize and improve some recent works of Caglar et al. , Xu et al. , and other authors.