Wave reconstruction and prediction aims to realize the reduction and forecasting of transient wave heights on the ocean surface, and the method can provide forward-looking information for ship navigation and reduce the risk of offshore operations. Marine microwave radar is an emerging tool currently used for accurate wave measurements that can be used to advance wave reconstruction and prediction. The wave reconstruction and prediction algorithm based on regularized least squares was proposed. Firstly, the wave model parameter matrix was estimated using the regularized least squares method based on the radial velocity space-time matrix and the propagation operator matrix of the water particle acquired by the marine microwave radar, and the introduction of the regularization parameter ensures the stability of the parameter solution. Then, based on the linear wave propagation model, the instantaneous wave heights at the sea surface were reconstructed or predicted for different airtime positions. In the numerical simulation experiments, the distribution law of the wave predictable zone was analyzed, and the reconstruction and prediction performance of the proposed method was evaluated under different sea conditions, and the results show that the reference wave height matches the predicted wave height very well within the predictable zone, which proves that the proposed method has a good wave reconstruction and prediction performance.