According to the motion style, a nanomotor can be classified into linear nanomotor and rotary nanomotor. Nanomotors, as the core components of nanomachine, have broad research prospects and applications. Here, a molecular dynamics method is used to simulate the linear nanomotor on a stretched carbon nanotube substrate. The results show that the nanomotor speed is well controlled by the temperature gradient, the axial strain of the substrate and the nanomotor size. When the nanomotor moves stably on the substrate carbon nanotube with a temperature difference of 200 K at both ends, the time required for the nanomotor to travel the same distance on the substrate carbon nanotube with 15% strain is about 62% longer than that without strain. The mechanism for the nanomotor movement and speed control is attributed to the thermophoretic force acting on the nanomotor. Specifically, the thermophoretic force increases with increasing substrate temperature gradient and decreases with increasing substrate strain. These results provide a novel method for controlling the speed of a nanomotor and inform nanomotor design and manufacture, as well as presenting a deeper understanding of the mechanism and movement law of the nanomotor.