Rate compatibility of forward error correction codes is required to accomplish high throughput and reliability over time-varying wireless channels. The grouping and sorting (GS) algorithm can produce rate-compatible puncturing LDPC (RCP-LDPC) codes with good performance. However, there is a limit in the achievable highest puncturing rate. In this paper, a novel layer-by-layer sorting algorithm is proposed to design RCP-LDPC without any limitation in the highest puncturing rate. The algorithm can be applied to an arbitrary LDPC code to obtain a code rate infinitely close to one. Simulation over AWGN channels shows that the proposed algorithm has superior performance as compared to the GS algorithm.