In this paper, we introduce a new certain subclassN(α, λ, t) of Non-Bazilević analytic functions of type (1 − α) by using the Chebyshev polynomials expansions. We investigated some basic useful characteristics for this class, also we obtain coefficient bounds and Fekete-Szegö inequalities for functions belong to this class. This class is considered a general case for some of the previously studied classes. Further we discuss its consequences.