A novel simplifying Volterra structure algorithm is proposed for intensity modulation direct detection (IM-DD) optical fiber short distance communication system by using the decision feedback equalization algorithm (DFE). Based on this algorithm, the signal damage for four-level pulse amplitude modulation signal (PAM-4) is compensated, which is caused by device bandwidth limitation and dispersion during transmission. Experiments have been carried out using a 25GHz Electro-absorption Modulated Laser (EML), showing that PAM-4 signals can transmit over 10km in standard single-mode fiber (SSMF). The 112Gbps and 128Gbps signals can reach the error rate threshold of KP4-FEC (BER=2*10-4) and HD-FEC (BER=3.8*10-3), respectively. The simplified principle and process of proposed Volterra-based equalization algorithm are presented. Experimental results show that the algorithm complexity is greatly reduced by 75%, which provides an effective theoretical support for the commercial application of this algorithm.