The quest for reliable vehicle navigation in urban environments has led the integration of Light Detection and Ranging (LiDAR) Odometry (LO) with Global Navigation Satellite Systems (GNSS) and Inertial Measurement Units (IMU). However, the performance of the integrated system is limited by a lack of accurate LO error modeling. In this paper, we propose a weighted GNSS/IMU/LO integration-based navigation system with a novel LO error model. The Squared Exponential Gaussian Progress Regression (SE-GPR) based LO error model is developed by considering the vehicle velocity and number of point cloud features. Based on error prediction for GNSS positioning and LO, a weighting strategy is designed for integration in an Extended Kalman Filter (EKF). Furthermore, error accumulation of the navigation state, especially in GNSS-challenging scenarios, is restrained by the LiDAR-Aided Lateral Constraint (LALC) and Non-Holonomic Constraint (NHC). An experiment was conducted in a deep urban area to test the proposed algorithm. The results show that the proposed algorithm delivers horizontal and three-dimensional (3D) positioning Root Mean Square Errors (RMSEs) of 3.669 m and 5.216 m, respectively. The corresponding accuracy improvements are 35.9% and 50.0% compared to the basic EKF based GNSS/IMU/LO integration.