This paper considers the data association problem for multi-target tracking. Multiple hypothesis tracking is a popular algorithm for solving this problem but it is NP-hard and is is quite complicated for a large number of targets or for tracking maneuvering targets. To improve tracking performance and enhance robustness, we propose a randomized multiple model multiple hypothesis tracking method, which has three distinctive advantages. First, it yields a randomized data association solution which maximizes the expectation of the logarithm of the posterior probability and can be solved efficiently by linear programming. Next, the state estimation performance is improved by the random coefficient matrices Kalman filter, which mitigates the difficulty introduced by randomized data association, i.e., where the coefficient matrices of the dynamic system are random. Third, the probability that the target follows a specific dynamic model is derived by jointly optimizing the multiple possible models and data association hypotheses, and it does not require prior mode transition probabilities. Thus, it is more robust for tracking multiple maneuvering targets. Simulations demonstrate the efficiency and superior results of the proposed algorithm over interacting multiple model multiple hypothesis tracking.