This paper, by proposing a wheel-LiDAR method of odometry and mapping(WLOAM), using wheel encoder, steering encoder,LiDAR, and optional GPS for autonomous vehicles, estimates the low-drift pose at real-time and builds a high-accurate map. The odometry consists of the wheel odometry algorithm and the LiDAR odometry algorithm. The former estimates the 3-DOF ego-motion of LiDAR at a high frequency based on Ackermann steering geometry, whose resulting pose increment is applied in point clouds de-skewing and works as a fine initial guess for LiDAR odometry while the latter performs the 6-DOF scan-to-map LiDAR pose optimization at a relatively low frequency to compensate the pose error accumulated by the wheel odometry, whose core is a two-stage method with an angle-based metric for extracting features. The mapping method is based on the factor graph consisting of the LiDAR odometry factor, the loop closure factor, and the optional GPS factor, which is solved via incremental smoothing and mapping (iSAM) to produce a global map online. An auto-aligned-GPS-factor is proposed for fusing GPS measurement incrementally without explicit initialization. The proposed method was extensively evaluated on the datasets gathered from the autonomous vehicle platform and compared with related open-sourced works. The results show a lower drift rate, which reaches 0.53% in the largest test described in this paper. The implementation of the proposed method is open-sourced for communication (https://github.com/Saki-Chen/W-LOAM).