Abstract: A construction scheme of reversible Quasi Cyclic-Low Density Parity Check (QC-LDPC) codes is proposed by setting rationally zero matrices. This solves the problems of singular check matrix and high encoding complexity in conventional QC-LDPC codes. With circulant matrix corresponding to polynomial in finite fields, the scheme exploits the extended version of Euclid's algorithm to conquer the problem of QC-LDPC construction rate lager than design rate. Moreover, in the encoding process, first dividing the check matrix into blocks, and then the extended version of Euclid's algorithm is used to invert a circulant matrix, it results in dynamic complexity decrease. EXtrinsic Information Transfer (EXIT) chart implies the convergence of decoder. More simulations illustrate that the performance of the proposed construction structure is better than random LDPC when the code length is short, which is suitable for UnderWater Acoustic Communication (UWAC). Finally, applying QC-LDPC to Zero Padding-Orthogonal Frequency Division Multiplexing (ZP-OFDM) for evaluating the performance in UWAC, extended simulation shows that the reversible QC-LDPC codes can dynamically improve the system robustness.