In this paper, we consider both one-period and multi-period distributionally robust mean-CVaR portfolio selection problems. We adopt an uncertainty set which considers the uncertainties in terms of both the distribution and the first two order moments. We use the parametric method and the dynamic programming technique to come up with the closed-form optimal solutions for both the one-period and the multi-period robust portfolio selection problems. Finally, we show that our approaches are efficient when compared with both normal based portfolio selection models, and robust approaches based on known moments.