As an important field of robot research, robot path planning has been studied extensively in the past decades. A series of path planning methods have been proposed, such as A* algorithm, Rapidly-exploring Random Tree (RRT), Probabilistic Roadmaps (PRM). Although various robot path planning algorithms have been proposed, the existing ones are suffering the high computational cost and low path quality, due to numerous collision detection and exhausting exploration of the free space. In addition, few robot path planning methods can automatically and efficiently generate path for a new environment. In order to address these challenges, this paper presents a new path planning algorithm based on the long-short term memory (LSTM) neural network and traditional RRT. The LSTM-RRT algorithm first creates 2D and 3D environments and uses the traditional RRT algorithm to generate the robot path information, then uses the path information and environmental information to train the LSTM neural network. The trained network is able to promptly generate new path for randomly generated new environment. In addition, the length of the generated path is further reduced by geometric relationships. Hence, the proposed LSTM-RRT algorithm overcomes the shortcomings of the slow path generation and the low path quality using the traditional RRT method.