This paper discusses the optimum design of tuned mass damper (TMD) for seismically excited building structures. In the design process the multi degree of freedom structures are considered so that it makes improvement to the available design procedures so far, where usually only single mode model is considered. The H2 norm of the transfer function from the external disturbance to a certain regulated output is taken as a performance measure of the optimization criterion. The genetic algorithm, which has been successfully applied in many applications, is used to find the optimum value of TMD parameters. The numerical examples for optimum parameters of TMD for multi degree of freedom structures are presented to show the effectiveness of this design procedure. It is shown that by using the proposed procedure, the optimum value of the mass damper can be determined without specifying the modes to be controlled. A comparison is also made to the Den Hartog and Warburton approaches.