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In order to meet the increasing requirements of speed and distance, an advanced digital signal processing (DSP) algorithm is preferred without changing the system structure in intensity modulation and the direct detection (IM/DD) system. As the transmission distance increases, the power fading induced by dispersion must be mitigated. In addition, linear and nonlinear inter symbol interference (ISI) introduced by bandwidth limitation and device imperfections becomes an obstacle to achieving higher capacity. The Gerchberg–Saxton (GS) algorithm was recently used to compensate for dispersion. In this paper, GS-based pre- and post-compensation schemes in the IM/DD system with nonlinearity were investigated. We investigated and compared the performance of the GS-based pre- and post-compensation algorithm in a 28 GB aud four-level pulse amplitude modulation (PAM-4) transmission over 40 km standard single-mode fiber (SSMF). The bit error rate (BER) achieved a threshold of 3.8 × 10−3 using look-up-table (LUT), FFE, and the GS-based pre-compensation algorithm without iterations. Turning to the GS-based post-compensation scheme, 80 iterations are needed. However, the demand for FFE is reduced. The algorithm selection depends on the tolerance of the transmitter or receiver complexity in specific scenarios. The joint LUT and GS-based pre-compensation algorithm may be a preferable approach in scenarios where a low-complexity receiver is desired.