A curved track-TRD analytical model is established in this paper. The TRD has two natural frequencies and the curved track is simulated by the discretely supported Timoshenko beam based on the theory of infinite-periodical structure. By using mode superposition method in frequency domain，the dynamic response of one point on the track can be obtained by calculating the track dynamic response at the corresponding point in a basic cell. After obtaining the dynamic response of the curved track-TRD model，some conclusions can be drawn. TRD is effective on controlling the track vibration in a broad frequency range and restraining the pinned-pinned resonance of the track. The rail decay rate increases after the TRD is installed. TRD can restrain the dynamic response of tracks with different radius. The dynamic response of the track under a moving harmonic load is reduced when the load frequency is higher than the first order natural frequency of the track. The vibration response of the track is significant reduced when the excitation frequency of the moving load is equal to the natural frequencies of the TRD or the frequency of the track pinned pinned resonance.