The main purpose of the multiple target tracking is jointly estimating the number of targets and their states from a sequence of observation sets, which has the feature of association uncertainty, detection uncertainty, noise and false alarms. In the view of the data association of traditional multiple target tracking algorithm, the large amount of calculation is hard to achieve, while the PHD filter algorithm based on random sets can avoid the problems mentioned above and can estimate the status directly. At present, there is no closed form of solution for the PHD recursion algorithm. This work shows that when both the target dynamics and birth process are linear Gaussian models, the posterior intensity at any time step is a Gaussian mixture. Therefore, the recursive equation can be derived, which can represent the mean of the posterior intensity in terms of Gaussian components, variances and weights. It is demonstrated by simulation that this algorithm can track multiple targets well under non linear, Gaussian assumption.