Deep neural network (DNN) inference task offloading is an essential problem of edge intelligence, which faces the challenges of limited computing resources shortage of edge devices and the dynamics of edge networks. In this article, the DNN inference task offloading problem in queue‐based multi‐device and multi‐server collaborative edge computing is investigated. To support efficient collaborative inference, we formulate a multi‐objective optimization problem that minimizes the average delay and maximizes average inference accuracy. Due to time‐varying queue load states and random task arrival, it is challenging to solve this optimization problem. Thus, a deep reinforcement learning based task offloading algorithm, named LSTM‐TD3, is proposed to solve the formulated problem. Specifically, LSTM‐TD3 incorporates the long short‐term memory (LSTM) and twin delayed deep deterministic policy gradient algorithm (TD3), and can leverage long‐term environment information to efficiently explore the optimal task offloading solution. Finally, we compared the performance of LSTM‐TD3 with TD3 (without LSTM) and random offloading algorithms, and simulation results show the LSTM‐TD3 reduce the average inference delay by up to 21.6%, and the accuracy is better than other algorithms.