A decision feedback equalization (DFE) algorithm is proposed by simplifying Volterra structure. The simplification principle and process of the proposed Volterra-based equalization algorithm are presented. With the support of 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 in C-band intensity modulation direct detection (IM-DD) fiber system. Experiments have been carried out to demonstrate that PAM-4 signals can transmit over 2 km in standard single-mode fiber (SSMF) based on a 30 GHz Mach-Zehnder modulator (MZM). The bit error rate (BER) can reach the threshold of hard decision-forward error correction (HD-FEC) (BER=3.8×10-3) and its sensitivity is reduced by 2 dBm compared with traditional feedforward equalization (FFE). Meanwhile, the algorithm complexity is greatly reduced by 55%, which provides an effective theoretical support for the commercial application of the algorithm.