Recently, many researchers have tried to design a system for indoor illumination because the benefits of solar systems. A simple parabolic reflector is often used to collect sunlight but the efficiency is poor when sunlight isn't incident normally. Therefore, an accurate machine to track sun has to be used. In order to get better tolerance, a light pipe based solar concentrator (LPBSC) which comprises a parabolic reflector and a hollow reflective light pipe is proposed. We develop a math model which combines the reflection times of sunlight in light pipe and the candela data of parabolic reflector to analyze the efficiency. And then, straight light pipe is replaced by tapered light pipe to improve the tolerance. Optical simulation software, TracePro, and mathematical software, MATLAB, are used to prove the model is correct and feasible. In the results, LPBSC can improve the tolerance to get good efficiency.