Abstract: In this paper, we introduce and investigate a new subclass of k-fold symmetry close-to-convex functions in the open disc. For functions belonging to the above subclass, firstly we drive several properties including integral expression, coefficient estimates and distortion theorems using subordination and primary method. The results obtained generalize some known results. Finally, with the help of the linear topological space theory, we further discuss the end-point property and get some interesting new results.