In this paper, a memory polynomial equalizer combined with decision feedback equalizer (MPE-DFE) is proposed to eliminate channel distortions for intensity modulation and direct detection (IM/DD) systems. Compared with traditional feedforward equalizer and decision feedback equalizer (FFE-DFE), the proposed MPE-DFE introduces extra square terms and cubic terms to jointly equalize chromatic dispersion and nonlinear distortions. We demonstrated a C-band 56-Gb/s four-level pulse-amplitude modulation (PAM4) system over 80-km standard single mode fiber (SSMF) transmission. Experimental results show that the proposed MPE-DFE achieved up to 6.2 dB higher SNR than traditional FFE-DFE. Moreover, the achieved bit error ratio (BER) with MPE-DFE reaches 3.1 × 10-3, which is below 7% feedforward error correction (FEC) threshold of 3.8 × 10-3. To the best of our knowledge, we achieved a record transmission distance for C-band 56-Gb/s PAM4 signal with only electrical equalization at the receiver.