The relay channel is the common approach to cooperative communication. Quasi-cyclic low-density parity-check (QC-LDPC) code design for the relay channel is important to cooperative communication. This paper proposes a bilayer QC-LDPC code design scheme for the relay channel. Combined with the bilayer graphical code structure, an improved Chinese remainder theorem (CRT) method, the Biff-CRT method is presented. For the proposed method we introduce a finite field approach. The good performance of the finite field based QC-LDPC code can improve the performance of its corresponding objective QC-LDPC code in the proposed scheme. We construct the FF code and the FA code by the Biff-CRT method. The FF code and the FA code are both named as their two component codes. For the FF code, the two component code are both finite field based QC-LDPC codes. For the FA code, one of the component codes is the finite field based QC-LDPC code and the other is the array code. For the existing CRT method, the shortened array code and the array code are usually used as the component codes to construct the SA code. The exponent matrices of FF code, FA code and SA code are given both for the overall graph and the lower graph. Bit error rate (BER) simulation results indicate that the proposed FF code and FA code are superior to the SA code both at the relay node and the destination node. In addition, the theoretical limit and the BER of the bilayer irregular LDPC code are also given to compare with the BER of the proposed QC-LDPC codes. Moreover, the proposed Biff-CRT method is flexible, easy to implement and effective for constructing the QC-LDPC codes for the relay channel, and it is attractive for being used in the future cooperative communication systems.