In this paper, an optimum TCM(trellis coded modulation)combined with CPM(continuous phase modulation) signal is investigated, and the performances are evaluated on the two-ray fading channel, which is one of the well-known frequency-selected because of their relatively good power and spectrum efficiency, and the modulation index is varied from 0.1 to 0.6. The performance is evaluated for each modulation index. The constraint length of the encoder, which is comprised in TCM, is chosen to be 2 and 3. From the performance evaluations, when the constraint length is 3 and modulation index 0.5, a power gain if the optimum TCM over the scheme without coding is observed to be 2.0dB for 1REC and 2.1dB for 3RC, respectively, on the fading channel. Thus, a significant improvement on the line quality is expected when the optimum TCM presented in this paper is employed in digital mobile radio applications.