Propeller-crossing probability analysis is crucial for evaluating the impact resistance and foreign object exclusion capability of turboprop engines. However, due to the complex structure of the propeller and the uncertainties associated with the impact location as well as the flight attitude of the foreign object, developing a comprehensive model for analyzing the propeller-crossing process remains a significant challenge. This paper presents a novel simulation method that can obtain the probability of a foreign object successfully crossing the propeller using a high-fidelity structure model of the propeller and a comprehensive substituted model of the foreign object. To validate the performance of the proposed method, an analytical model is developed that takes into account the spatial structure constraints of the propeller and the foreign object. The proposed method is applied to calculating the probability of bird ingestion, and the results reveal that the increments in flight speed and aspect ratio of the bird have opposite effects on the propeller-crossing probability, and the values eventually converge to a constant value.