In order to lower the error floor of LDPC (low-density parity-check) codes, a new class of APPS-LDPC (arithmetic progression and partition shift LDPC) codes was proposed. The APPS-LDPC codes are based on cycle path description theory with arbitrary code length, code rate, column weight. The girth of their Tanner graph is at least eight. Cyclic shift coefficients can be described in simple analytic expressions to reduce required memory usage. The simulation results show that the proposed APPS-LDPC code (496,248) gets a coding gain of 1.9 dB at least compared to the PEGLDPC (progressive edgegrowth LDPC) code at BER (bit error rate) 10^-5. And at high signal to noise ratio region, the gap between two decoding curve increases gradually. Besides, APPS-LDPC code (6144, 5376) whose column degree is 3 gets a coding gain of 0.25 dB at least compared to the PS-LDPC code at BER 10^-8, and there′s no obvious error floor phenomenon when the signal to noise is above 4.6 dB. The performance of the proposed algorithm also outperforms the 4-girth or the 6-girth PEG-based LDPC codes, especially in error floor region. The time-consuming and complexity for constructing an APPS-LDPC code also show some advantages over PS-LDPC code and PEG-LDPC code. And through trapping sets searching method based on Tanner graph, there is no small trapping set composed by cycle 8 in (496,248) APPS-LDPC code, which demonstrates the reduction of the error floor.