When tracking the velocity of a snake-like robot with passive wheels, the dynamics equations are complex and not convenient for controller design by the classical dynamics modeling method. In this paper, the dynamics equations are projected into the velocity distribution space and a dynamics and control unified model is derived which is easier for the controller designing. Since, singular postures always occur. When tracking the velocity of the snake-like robot, a disturbance velocity is introduced. Based on the disturbance velocity and the unified model, a velocity tracking control algorithm, avoiding the singular posture, is proposed. The torques can be derived from the inverse dynamics to control the snake-like robot. Numerical simulations and experiment for the velocity tracking of the desired velocity are presented to show that the proposed algorithm can track the desired velocity and validly avoid the singular postures at the same time.