This paper investigates the task how to achieve fairness in distributed dynamic spectrum access (DSA). Specifically, we consider a cognitive radio network scenario with multiple primary users (PUs) and secondary users (SUs). Each PU operates in a licensed channel. We assume that there is no coordination between PUs and SUs, and no coordination among SUs. The key challenges for SUs are to: (1) avoid collisions with PUs, (2) avoid collisions with other SUs, (3) fair access of spectrum resources in an uncoordinated system, (4) deal with different PU activity patterns, (5) deal with spectrum sensing errors. To address these challenges, we propose a deep reinforcement learning (DRL) approach and an associated reward function to achieve fair access to spectrum resources. Specifically, we use the method of Dueling Double Deep Q-Networks with Prioritised Experience Replay (D3QN-PER) as DRL algorithm for each SU. In our simulation experiments, we demonstrate that the proposed approach performs better than existing DRL methods.