In order to measure the uncertainty of the stochastic systems subjected to arbitrary noise disturbance instead of Gaussian white noise, the minimum entropy control of tracking errors for dynamic stochastic systems is presented in this paper. Different from conventional hypothesis, it is assumed that the system output and noise obey multi-to-one mapping, which is more general in the practical application. A controller design was described based on minimizing system output error entropy and a recursive optimization algorithm was set up for dynamic, non-Gaussian and nonlinear system. This approach only used the formula of the probability density function of the tracking error to calculate the controller and it did not need to know the style of the system model and the probability density function of noise, which often is difficult to measure in fact. An illustrative example is utilized to demonstrate the efficiency of the minimum entropy control algorithm and the approving simulation results have been gained.