Hybrid Automatic Repeat reQuest(Hybrid ARQ) which is an excellent error control technique has been accepted as a key technique of 3GPP Long Term Evolution(LTE). Hybrid ARQ scheme based on Rate Compatible Punctured Turbo(RCPT) codes has outstanding performance and low implementation complexity, therefore this scheme has attracted wide concern. Traditional Hybrid ARQ schemes consist of Chase Combining based Hybrid ARQ(CC-HARQ) which has greater performance gain under higher channel SNR; and IR(Incremental Redundancy) based Hybrid ARQ which provides precise rate control under lower channel SNR. This paper proposes an Adaptive Selective Combining Hybrid ARQ(ASC-HARQ) which adaptively chooses CC-HARQ or IR-HARQ according to different channel SNR, while the receiver adaptively combines selected code blocks with high reliability. This paper analyzes the scheme’s performance in Rayleigh fading channel. Simulation results are given to compare the performance of this novel scheme with that of CC-HARQ and IR-HARQ. According to the simulation results, this scheme performs better than traditional schemes with similar complexity.