Mobile communication systems have been adopting link adaptive transmission schemes such as adaptive modulation and coding (AMC) and hybrid-ARQ (HARQ). Several wireless mobile communication systems have considered highly efficient incremental redundancy (IR) hybrid ARQ scheme. However IR-HARQ with LDPC codes has not been specified yet. In this paper, we propose an IR-HARQ scheme with rate compatible LDPC codes which adopts the notion of k-SR node and the propagation rate of soft output. Based on the design rule of rate compatible LDPC codes, we define the transmission priority of code bits and propose the sub-packet construction rule. We present the throughput performance of IR-HARQ with various modulation and coding and multi-antenna modes. Consequently, the proposed scheme provides the improvement of system throughput by elaborate link adaptation with CQI information.