Aiming at the problem that quasi-cyclic low density parity check (QC-LDPC) codes may have the error floor in the high signal to noise ratio (SNR) region, a new construction method of the QC-LDPC codes with the low error floor is proposed. The basic matrix of the method is based on the progressive edge growth (PEG) algorithm and the improved eliminate elementary trapping sets (EETS) algorithm so as to eliminate the elementary trapping sets in the basic matrix, then the Zig-Zag method is used to construct the cyclic shift matrix which is used to extend the basic matrix in order to construct the parity check matrix. The method not only can improve the error floor in the high SNR region, but also can flexibly design the code length and code rate. The simulation results show that at the bit error rate of 10-6, the PEG-trapping-Zig-Zag (PTZZ)-QC-LDPC(3024,1512) codes with the code rate of 0.5, compared with the PEG-Zig-Zag (PZZ)-QC-LDPC(3024,1512) codes and the PEG-QC-LDPC(3024,1512) codes, can respectively improve the net coding gain of 0.1 dB and 0.16 dB. The difference among the bit error rate performance curves will become better with the increase of the SNR. In addition, the PTZZ-QC-LDPC(3024,1512) codes have no error floor above the SNR of 2.2 dB.