Abstract: In this paper we introduce a new subclass $\mathcal{R}^*(p,g,\psi,\varrho,\beta,\phi,\gamma,\zeta)$ of $p$-valent functions with negative coefficient defined by Hadamard product associated with a generalized differential operator. Radii of close-to-convexity, starlikeness and convexity of the class $\mathcal{R}^*(p,g,\psi,\varrho,\beta,\phi,\gamma,\zeta)$ are obtained. Also, distortion theorem, growth theorem and coefficient inequalities are established.