As a rule, when a crack happens in composite materials, the fibrous system will generate bridging fibers resulted in the asymmetrical extending of the crack. In this paper, a dynamic asymmetrical crack model of bridging fiber pull-out in unidirectional composite materials is built for analyzing the distributions stress and displacement with the internal asymmetrical crack under the loading conditions of an applied non-stress and the traction forces on crack faces yielded by the bridging fiber pull-out model. Thus the fiber failure is determined by the maximum tensile stress, the fiber ruptures, and hence the crack propagation should also occur in self-similar modality. The formulation involves the development of a Riemann-Hilbert problem. The analytical solution of an asymmetrical extension crack in unidirectional composite materials under the conditions of moving increasing loads $Pt^2/x^2$ and $Px^2/t$ is concluded, respectively. Based on relative material properties, the variable law of dynamic stress intensity factors was depicted perfectly. After the conclusion of analytical solutions with the superposition theorem, the solutions of arbitrary complex problems could be acquired.