Superconducting materials are always severely restricted in practical engineering applications due to the degradation of superconductivity under external mechanical loads. Based on the damage theory of fragile fiber reinforced metal matrix composites and the Weibull distribution function, a degradation model to describe the mechanical deformation influence of the Bi-based superconducting multi-filamentary composite tape on its critical current under axial load was proposed. The critical currents of superconducting tape with the axial strain in the processes of axial loading and unloading were analyzed. The degradation of the critical current of superconducting tape under the conditions of different initial damages and pre-strains was predicted theoretically. It is shown that the theoretical model we developed can predict well the degradation of critical current of the Bi-based superconducting multi-filamentary composite tape with axial strain. The results are in good agreement with the experimental data. The present investigation will be helpful for superconducting composites in applications.