This paper develops a novel approach for automatic parameter calibration of soil constitutive models by combining Bayesian optimization (BO) and genetic algorithm (GA). The BO method enables locating the possible point over a large multi-parameter search domain quickly, by which the search domain is no longer required to be accurately pre-defined. Thereafter, the GA is employed to find the best solution within the BO-optimized search space. This calibration procedure can quickly give the best-matched model parameters for both sands and clays even with the same large search space. Taking a critical state-based soil model (Clay And Sand Model (CASM)) as an example, the superiority and capability of the proposed calibration method are examined by comparing experimental data with predicted results for both clays and sands. It is shown that the BO-GA-based approach can reduce errors by 46.4% for clays and 41.2% for sands compared with the conventional GA method and outperforms other traditional optimization algorithms. Eventually, the evolution process of BO and GA is visualized to better understand the principles of automatic parameter calibration, which is followed by model uncertainty analyses.