By incorporating the semi-Markov process into a bayesian estimation scheme, an adaptive state estimator is developed. This estimator can prevent the loss of the target tracking when a target makes a sudden radical change in its flight trajectory. A method of compensating for the uncertainty of the tracking performance is also presented. The covariance-matching technique is adopted such that the accuracy of the adaptive state estimator is improved. Several examples are given to illustrate the superior tracking performance, and this adaptive algorithm can easily be implemented on the digital computer with a little modification for different speeds.