Current studies that apply reinforcement learning (RL) to dynamic spectrum access (DSA) problems in wireless communications systems mainly focus on model-free RL (MFRL). However, in practice, MFRL requires a large number of samples to achieve good performance making it impractical in real-time applications such as DSA. Combining model-free and model-based RL can potentially reduce the sample complexity while achieving a similar level of performance as MFRL as long as the learned model is accurate enough. However, in a complex environment, the learned model is never perfect. In this article, we combine model-free and model-based RL, and introduce an algorithm that can work with an imperfectly learned model to accelerate the MFRL. Results show our algorithm achieves higher sample efficiency than the standard MFRL algorithm and the Dyna algorithm (a standard algorithm integrating model-based RL and MFRL) with much lower computation complexity than the Dyna algorithm. For the extreme case where the learned model is highly inaccurate, the Dyna algorithm performs even worse than the MFRL algorithm while our algorithm can still outperform the MFRL algorithm.