Slip detection plays a vital role in robotic manipulation and it has long been a challenging problem in the robotic community. In this paper, we propose a new method based on deep neural network (DNN) to detect slip. The training data is acquired by a GelSight tactile sensor and a camera mounted on a gripper when we use a robot arm to grasp and lift 94 daily objects with different grasping forces and grasping positions. The DNN is trained to classify whether a slip occurred or not. To evaluate the performance of the DNN, we test 10 unseen objects in 152 grasps. A detection accuracy as high as 88.03% is achieved. It is anticipated that the accuracy can be further improved with a larger dataset. This method is beneficial for robots to make stable grasps, which can be widely applied to automatic force control, grasping strategy selection and fine manipulation.