This letter presents a new method for constructing rate-compatible low-density parity-check (RC-LDPC) codes, which is based on combining algebraic-based and graph-based construction methods. We first use a graph-based tool, protograph extrinsic information transfer chart, to construct a masking matrix. Then, the parity-check matrices of RC-LDPC codes are determined in accordance with the framework of the algebraic-based method. The proposed codes own a quasi-cyclic structure, and thus have advantages in hardware implementations of encoder and decoder. Simulation results show that the codes can achieve good bit error rate performance in the waterfall region within a wide range of code rates.