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With the aim to enhance the capability of predicting cavitating flows for Schnerr-Sauer model, a developed cavitation model was proposed based on an improved spherical bubble dynamic model and the homogeneous flow assumption. In particular, the terms of the second derivative of bubble radius and surface tension were also considered in the simplified Rayleigh-Plesset equation to give more reliable physical model for bubble shrink and growth. Unsteady and turbulent cavitating flows over a two-dimensional Clark-Y hydrofoil were calculated by using the proposed model and Schnerr-Sauer model in which a modified filter-based model was adopted for the turbulence modeling. The cavity shape evolution and the characteristics of hydrodynamic coefficient at different cavitation numbers were obtained from simulations. Comparing with available experimental data in the literature, for quasi-static sheet cavitation, the length of the sheet cavity as predicted by the proposed model almost remained unchanged and noticeable vapor-liquid interface was captured at the rear of the sheet cavity as well, which agreed better with the experiment description. For the periodic cloud cavitation, the cavitation area predicted by the proposed model was larger than that of the Schnerr-Sauer model, which was induced by the non-condensable gas and turbulence fluctuation considered in the proposed model. Moreover, the transient lift coefficient predicted by the proposed model agreed better with the experimental data and the proposed model had better capability than the Schnerr-Sauer model to predict some detailed features of the cyclic cavity evolutions in cloud cavitation. The overall results proved the reliability and accuracy of the improved cavitation model in cavitating flow simulations over a hydrofoil.