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Turbo code has been used by multiple communication standards due to its performance near Shannon limit. However, its decoding algorithm is complicated. Through the research on Turbo code, a novel design of Turbo decoder is presented in this paper. Turbo code is decoded by the Min-Sum decoding algorithm of LDPC code, which is a low complicated decoding algorithm. Moreover, messages are stored compressively, and the check-to-variable messages and the variable-to-check messages are stored alternately. This design reduced the required memory significantly. Finally, the decoder is simulated by ModelSim SE6.0 and the simulation results show that the decoder has high decoding speed.