We present a particle filter for multi-object tracking that is based on the ideas of the Approximate Bayesian Computation (ABC) paradigm. The main idea is to avoid the explicit computation of the likelihood function by means of simulation. For this purpose, a large amount of particles in the state space is simulated from the prior, transformed into measurement space, and then compared to the real measurement by using an appropriate distance function, i.e., the OSPA distance. By selecting the closest simulated measurements and their corresponding particles in state space, the posterior distribution is approximated. The algorithm is evaluated in a multi-object scenario with and without clutter and is compared to a global nearest neighbour Kalman filter.