The robust dynamic topology optimization of a continuum planar structure is studied to reduce its natural frequency variation when the structural material parameter uncertainties are considered. The uncertainties of the material properties are represented with the uncertain-but-bounded interval variables based on the non-probabilistic convex model. The dynamic topology optimization model for maximizing the first natural frequency is constituted by mitigating its variation，such that the robust optimization problem can be simply solved into a single-level framework. By the derivative analysis of the material parameters，a quadratic Taylor series expansion of the first natural frequency is obtained，and the design sensitivity of the natural frequency is accordingly evaluated in an explicit form under the uncertain material properties. By means of the material density-based strategy，the robust dynamic topology optimization is implemented with the material volume constraint，and the results are compared with those of the deterministic topology optimization. Optimal results show that the first-order natural frequency obtained with the proposed method has a higher robustness against the material property uncertainties，which fully demonstrates the importance of considering the uncertainties of the material parameters in the structural design stage.