Topology optimization design problem for planar continuum structure with the randomness of both the geometry and physical parameters under the structural foundamental frequency constraint is studied. Mathematical model of topology optimization design with random structure is established, in which the minimum the mean of structural weight is taken as objective function, the structural shape topology information is taken as design variables, the probabilistic reliability index of structural foundamental frequency is taken as constraint conditon. The computational expressions of the mean value and mean variance of the structural dynamic response are presented by the algebra method. Evolutionary structural optimization method is used in the optimization. Through two examples, the rationality and feasibility of the optimization model and solving method are validated.