In this paper, a family of rate-compatible (RC) low-density parity-check (LDPC) convolutional codes can be obtained from RC-LDPC block codes by graph extension method. The resulted RC-LDPC convolutional codes, which are derived by permuting the matrices of the corresponding RC-LDPC block codes, are systematic and have maximum encoding memory. Simulation results show that the proposed RC-LDPC convolutional codes with belief propagation (BP) decoding collectively offer a steady improvement on performance compared with the block counterparts over the binary-input additive white Gaussian noise channels (BI-AWGNCs). © 2016, Shanghai Jiaotong University and Springer-Verlag Berlin Heidelberg.