Tube hydroforming with radial crushing is a new tube hydroforming process to manufacture very long components with complex cross sections. A loading path is generally considered a major factor that greatly affects the formability of a component by tube hydroforming. In this study, the tube hydroforming with radial crushing process of a square cross-sectional component was investigated by using the finite element method, and a method to predict the optimal loading path for the tube hydroforming with radial crushing process was developed from the finite element simulation. A multi-object function was first built in terms of the die-filling ability, cross-sectional symmetry, and wall thickness uniformity. Subsequently, a multi-strategy approach, characterized by a genetic algorithm and the bisection method, was developed to predict the optimal loading path. The effectiveness of the prediction method was verified by comparing the formability of components deformed under the optimal and conventional loading paths. Furthermore, the developed multi-strategy approach was demonstrated to have high efficiency when the total calculation times for the multi-strategy approach and for genetic algorithm alone were compared.