Column is one of the core components of the machine tool，which dynamic characteristics is one of the important factors which determine the processing accuracy of super precision machine. By taking a study object of column structure of grinding machine with precision optical fiber micro-V channel, through exerting harmonic response force on cutter grinding point of column structure by the method of simulation experiment, the dynamic response parameters of column between 1 Hz and 175 Hz were obtained. By utilizing the central composite design and response surface methodology as well as multi-objective genetic algorithm, the largest harmonic response amplitude, the quality and the first order natural frequency of column structure were optimized as objective variables, and the praeto solution of column design variables was found out. The results show that after multi-objective optimized design, on the precondition that the weight of the column doesn’t increase, the maximum amplitude of response of the column is greatly reduced, consequently improved the dynamic stiffness of the columns and the processing precision of machine tools. 