Autonomous navigation in narrow indoor environments such as indoor factory, warehouse and laboratory environments, and so on requires higher flexibility and navigation accuracy of the vehicle. This article presents an autonomous navigation method for four-wheel steering vehicle which combines extended Kalman filtering (EKF) and rapidly-exploring random tree (RRT) to improve the precision and flexibility of autonomous navigation of the vehicle in narrow indoor environments. The four-wheel steering model was established by the key parameters such as shape size and minimum angle of rotation of the experimental vehicle. Considering the problem that the uncertainty of pose estimation increases with time during autonomous navigation, an error model is schemed by adding noise to the output terminal of the analog odometer sensor. In order to suppress the accumulation of the uncertainty and keep it stable for a long time, the prediction and update steps of Kalman filter are introduced to filter the error. Then, the simultaneous positioning and mapping are established. Based on accurate positioning, a set of driving paths to reach the target is generated by RRT sampling algorithm. The simulation results show that positioning uncertainty remains stable over time, which verifies the effectiveness of the method. The overall positioning percentage error is 0.21%. Compared with traditional dead reckoning algorithm, the positioning accuracy is improved by 73.1% and the vehicle flexibility is increased by 68.6%. The four-wheel steering vehicle can find an ideal trajectory in narrow indoor environments, which assures the efficiency of the autonomous navigation and the traveling quality of the navigation route. Finally, the experimental results are consistent with the simulation results, which further verifies the effectiveness of the proposed algorithm.