To solve the problem of spectrum scarcity and spectrum under-utilization in wireless networks, we propose a double deep Q-network based reinforcement learning algorithm for distributed dynamic spectrum access. Channels in the network are either busy or idle based on the two-state Markov chain. At the start of each time slot, every secondary user (SU) performs spectrum sensing on each channel and accesses one based on the sensing result as well as the output of the Q-network of our algorithm. Over time, the Deep Reinforcement Learning (DRL) algorithm learns the spectrum environment and becomes good at modeling the behavior pattern of the primary users (PUs). Through simulation, we show that our proposed algorithm is simple to train, yet effective in reducing interference to primary as well as secondary users and achieving higher successful transmission.