Curved section is regarded as the weak point of composite structures because of the delamination caused by the stress concentration. In the present work, L-shaped specimens made of randomly oriented short fiber-reinforced polypropylene were prepared to investigate the effect of the radius of the curved section of composite structures on the strength and the damage modes. The results of tensile tests and finite element analysis indicated that the radius greatly affects on the stress distribution and the damage modes, and showed good agreement with former researches using different composites. The strengths of the materials were extrapolated from the results of tensile tests and finite element analysis in this research. Finally, allowable radii of the curved section of the composite structures of two kinds of materials were given respectively.