Abstract In this paper, we introduce and investigate a subclass of analytic and bi-univalent functions which both f ( z ) {f(z)} and f - 1 ( z ) {f^{-1}(z)} are m-fold symmetric on the open unit disk. Furthermore, we find upper bounds for the initial coefficients | a m + 1 | {|a_{m+1}|} and | a 2 m + 1 | {|a_{2m+1}|} for functions in this subclass. The results presented in this paper generalize and improve some recent works