To investigate vibration control problem of structures with closely spaced frequencies, a typical symmetrical structure with two degree of freedom is taken as a case study. Parameter optimization and control performance of distributed tuned mass dampers(TMDs) for the vibration control of the structure with closely spaced modes are studied by using H2 performance criterion and gradient-based optimization method. Mathematical system model that combines the distributed TMDs and the structure is formulated to represent a closed loop system with a static output feedback control action. The gradient-based optimization method based on H2 performance criterion is extended to the parameter optimization of the distributed TMDs. To control the vibration with closely spaced modes, control output and nondimentional performance index are defined. Effect of modal control weighting forming the control output on the optimal parameters and the performance index is analyzed. The optimal weighting that can equalise two peak values of the performance index is specified. Then change regulations of the optimal parameters and the performance index against density of the closely spaced frequencies are formulated. Compared with classical design method of the TMDs, effective control performance of the distributed TMDs designed by H2 performance criterion is tested and verified. High efficiency of the gradient-based optimization method based on H2 performance criterion is confirmed especially when number of the distributed TMDs is enlarged.