GPS-based land vehicle navigation systems are subject to signal fading in urban areas and require aid from other enabling sensors. A low-cost gyro-free inertial navigation system (INS) without accumulated attitude errors and complicated initializations could be an effective solution to the problem. This paper investigates a Constrained Navigation Algorithm (CNA) and the Artificial Neural Network (ANN) technique to compensate velocity output from a gyro-free INS. The vehicle's heading will be calibrated by a full circle test so that the magnetometer's bias and scale factor error could be removed. Experiments with a vehicle driven over level terrain have been conducted to assess the performance of the compensated gyro-free INS solutions. The effect of the architecture of Neural Network on prediction performance has also been discussed as well as the applicability of the proposed solution to land vehicle navigation with GPS outages.