The standard Poisson multi-Bernoulli (PMB) filter for extended targets can hardly track spawning targets effectively. To resolve this problem, this study proposes an improved PMB tracking algorithm. The algorithm uses a random matrix method to model shapes and dimensions of extended targets and adopts a multi-hypothesis model to predict spawning targets in the filtering prediction stage and obtain multiple hypothetical components of gamma Gaussian inverse Wishart (GGIW). Finally, it updates the predicted components in the filtering update stage to estimate the motion state and expansion shapes of extended targets. Simulations show that the proposed algorithm has better tracking performance for spawning extended targets in comparison with the standard PMB filtering algorithm.