In this paper, a plane-based LiDAR odometry method is proposed. SLAM is an essential part of the autonomous robotic design that provides estimated pose of a robot. Instead of using the point cloud map as in most existing works, the proposed method constructs a map consisting of a series of planes for estimating the pose in an efficient and accurate way. The plane map method reduces the number of objects processed in the map compared to point cloud map methods. Every time a LiDAR scan is received, the scan is voxelized and the planes included are extracted. The planes are matched with their counterparts in the plane map. Subsequently, the pose is optimized iteratively to get an accurate pose estimate. With the optimized pose, the plane map is updated. The effectiveness of the proposed method is verified by both public datasets and real-world experiments. The results show that the plane map-based method can achieve accurate SLAM with a processing rate of more than 20 Hz in both indoor and outdoor scenarios in comparisons with some recent LiDAR SLAM algorithms.