Abstract: For multi–fidelity modelling in complex physical systems, conducting global sensitivity analysis serves as a critical tool for identifying the key design factors, out–loop optimization tasks, and uncertainty quantification. Classical variance–based global sensitivity analysis methods often fail to account for the relationship between the cumulative cost of low–fidelity samples and data heterogeneity, which may lead to unreasonable allocation of multi–fidelity sample sizes. A Cost–constrained Multi–fidelity Sensitivity Analysis (CMFSA) method is proposed. First, integrate unit cost differences and variance contribution to establish a multi–fidelity Gaussian process model (MFGP), realizing optimal initial sample allocation under a limited budget. Second, consider the heterogeneity of data with different fidelities to establish a layered expected improvement criterion (LREI), and carry out sequential sampling to optimize the local accuracy of the surrogate model. Finally, calculate Sobol sensitivity indices based on the multi–fidelity Gaussian process model to save computation resources. The method is verified on standard test cases and a HEG shock wind tunnel cylinder model. Numerical analysis results show that compared with the traditional method, the estimation error of Sobol sensitivity index by CMFSA is significantly reduced, and the computational efficiency is obviously improved.