An efficient decoding with low memory requirement is presented in this paper. With some extra memory bits，the proposed method could achieve nearly 2 times throughput compared with the conventional decoding. This paper combines min-sum decoding with Sliced Two-phase Message Passing (STMP) decoding, and proposes an overlapping scheme. The accessing of the operation units to the memory units is also discussed in order to analyze the access violation. A group of Low Density Parity Check(LDPC) codes are selected from Chinese Digital Television Terrestrial Multimedia Broadcasting(DTTB) standard，and the throughput gain as well as the ratio of extra memory bits for the proposed decoding over the conventional Two Phase Message Passing(TPMP) are calculated. The calculated results indicate that MS-STMP decoding needs only extra 44% memory bits to achieve 1.85 times throughput in even，which is more efficient than the Overlapped Message Passing(OMP) decoding.