In this letter, we propose a class of rate-compatible raptor-like protographs, which is aimed at the design of low-rate low-density parity-check (LDPC) codes with short length and fast convergence for ultra-reliable and low-latency communications in 5G. In the proposed protographs, the connection degrees can be progressively optimized by the protograph-based extrinsic information transfer analysis with a limited number of iterations. Following the protograph optimization, we construct the rate-compatible LDPC codes by a simplified error minimization progressive edge-growth algorithm and carry out simulations for performance comparisons. The simulation results show that our proposed LDPC codes have noticeable advantages over the existing low-rate LDPC codes with short length and limited numbers of decoding iterations.