This paper describes a multi-mode LDPC decoder which supports 19 block lengths and 6 code rates of Quasi-Cyclic LDPC code for Mobile WiMAX system. To achieve an efficient implementation of 114 operation modes, some design optimizations are considered including block-serial layered decoding scheme, a memory reduction technique based on the min-sum decoding algorithm and a novel method for generating the cyclic shift values of parity check matrix. From fixed-point simulations, decoding performance and optimal hardware parameters are analyzed. The designed LDPC decoder is verified by FPGA implementation, and synthesized with a $0.18-{mu}m$ CMOS cell library. It has 380,000 gates and 52,992 bits RAM, and the estimated throughput is about 164 ~ 222 Mbps at 56 MHz@1.8 V.