An iterative decoding algorithm of rate-compatible punctured low-density parity-check (RCP-LDPC) codes of high coding rates is developed. This algorithm performs a predetermined recovering process of punctured bits sums at the beginning of each iteration of the standard belief-propagation (BP) decoding algorithm. By propagating messages of two punctured bits sum, this algorithm can recover much more punctured bits than the standard BP decoding algorithm. It is shown that the proposed algorithm is applicable for RCP-LDPC codes of higher coding rates with little increase of decoding complexity.