Abstract: The topology optimization with frequency constraints is mainly focused on the continuum structures currently,however,the researches on topology optimization for frame structures with frequency constraints are relatively less. To obtain the optimal frame structures with frequency constraint,it is necessary to conduct research on the topology optimization for frame structures with frequency constraint.Based on ICM( independent,continuous and mapping) method,the zero-one type discrete topology variables are transformed into the continuous topology variables between zero and one. A continuous topology optimization model is established to minimize the weight with frequency constraint. Based on the behavior research of frequency constraints for frame structures, two different power functions were introduced as the filter function to explicit the frequency constraints approximately. The object and constraints were both expressed as the first-order Taylor expansions of topology variables to establish the linear programming model. The movable limits were adopted to control the step size of topology variables in order to avoid the iterative oscillation and ensure the optimization accuracy. The numerical examples show that the linear programming model based on ICM method can efficiently solve the topology optimization problem with base frequency constraint for frame structures.