Most of current extended target tracking algorithms assume that its system is linear Gaussian system. To track multiple extended targets for nonlinear Gaussian system, an multiple extended target tracking algorithm using particle filter to jointly estimate target state and association hypothesis was proposed. Firstly, the idea of joint estimation of the multiple extended target state and association hypothesis was proposed, which avoided mutual constraints in estimating target state and data association. Then, based on extended target state evolution model and measurement model, a joint proposal distribution function for multiple extended target and association hypothesis was established, and the Bayesian framework for the joint estimation was implemented by particle filtering. Finally, to avoid the dimension disaster problem in the implementation of the particle filter, the generation and evolution of the multiple extended target combined state particles were decomposed into that of the individual target state particles, and the particle set of each target was resampled according to the weight association with it, so that each target retained the particles with better state estimation while suppressing the poor part of target state estimation. Simulation results show that, in comparison with the Gaussian-mixture implementation of extended target probability hypothesis density filter and the sequential Monte Carlo implementation of that, the estimation accuracy of the target state is improved, and the Jaccard distance of shape estimation is reduced by approximately 30% and 20% respectively. The proposed algorithm is more suitable for multiple extended target tracking of the nonlinear system.