In this paper, we study right half-plane harmonic mappings f 0 and f , where f 0 is fixed and f is such that its dilatation of a conformal automorphism of the unit disk. We obtain a sufficient condition for the convolution of such mappings to be convex in the direction of the real axis. The result of the paper is a generalization of the result of by Li and Ponnusamy [11] , which itself originates from a problem posed by Dorff et al. in [7].