In this work, we present an adaptive reliability-driven conditional innovation (AR-CID) decoding algorithm for low-density parity check (LDPC) codes. The proposed AR-CID decoding algorithm consists of one stage of message quality checking and another stage of message passing refinement, which are incorporated into a residual belief propagation decoding strategy. An analysis of the AR-CID decoding algorithm is carried out along with a study of its computational complexity and latency characteristics. Simulation results for several examples of LDPC codes, including short and medium-length codes over an extended range of channel conditions, indicate that the proposed AR-CID decoding algorithm outperforms competing decoding techniques and has an extremely fast convergence, making it particularly suitable for low-delay applications.