We propose a quasi-linear trellis-coded modulation (TCM) using nonbinary convolutional codes for quadrature amplitude modulation (QAM). First, we study a matched mapping which is able to reduce the computational complexity of the Euclidean distances between signal points of MQAM. As an example, we search for rate R=1/2 convolutional codes for coded 64QAM by this method. The symbol error rates of the proposed codes are estimated by the distance properties theoretically and they are verified by simulation. In addition, we compare the minimum free Euclidean distances of these new codes with their upper bounds. Finally, the bit error probabilitiy of the proposed coded modulation is compared with uncoded signal constellations and a conventional TCM code proposed by Ungerboeck. The result shows the proposed scheme outperform them on the AWGN channels.