Abstract: The starlikeness of order \beta and strongly starlikeness for generalized non-Bazilevi\uc functions are investigated. Firstly, two lemmas of differential subordination are established. By applying differential subordination and differential inequality, some sufficient conditions are obtained for validating that generalized class of non-Bazilevi\uc functions are a subclass of starlike functions of order \beta or strongly starlike functions of order \gamma.