In complex environments where narrow passageways exist, there are problems such as low success rate of path finding in the path planning of mobile robots based on the traditional fast expanding random tree (RRT) algorithm. To address the above problems, an RRT algorithm for autonomous narrow channel finding is proposed, using an entrance finding algorithm to identify the entrance of the channel and a bias strategy to rationalize the sampling point selection to improve the success rate of path planning. In addition, a greedy algorithm is introduced to optimize the initial path and improve the quality of the planned path. Through experiments, it is shown that the proposed algorithm improves 59.6%, 56%, 9.3%, and 40% in four aspects compared with the RRT algorithm with bias in narrow channel environment in terms of iteration time, number of iterations, path length, and path planning success rate, respectively.