We experimentally demonstrate a novel nonlinearity-mitigation scheme based on a complex-valued neural network (CVNN) which is constructed by artificial neurons with complex-valued input and output. The in-phase (I) and quadrature (Q) components of optical signal are operated as complex values in the CVNN. A 40-Gbit/s optical 16QAM signal distorted by SPM was successfully compensated, improving error vector magnitude (EVM) by about 15%. The learning speed of the nonlinear equalizer was improved by using the CVNN, compared with conventional real-valued neural network (RVNN). Furthermore, the study show that CVNN has the potential to improve the computational complexity of RVNN.