When a crack occurs in composite materials, the fibrous system will form bridges, and the crack extends asymmetrically as a rule. In this paper an asymmetrical dynamic crack model of bridging fiber pull-out of composite materials is presented for analyzing the distributions stress and displacement under the loading conditions of an applied nonhomogenous stress and the traction forces. Thus the fiber failure is ascertained by maximum tensile stress, the fiber ruptures and hence the crack propagation should also appear in the modality of self-similarity. The formulation involves the development of a Riemann-Hilbert problem. Analytical solution of an asymmetrical propagation crack of composite materials under the conditions of an increasing force $Px^2/t^2$, $Pt^2/x$ is obtained respectively. After those analytical solutions were utilized by superposition theorem, the solutions of arbitrary complex problems could be gained.