The optically pumped magnetometer (OPM) operating in spin exchange relaxation-free (SERF) regime is a kind of magnetic sensor that has ultra-high sensitivity. SERF OPMs need to operate in a near zero magnetic field environment. In many applications, multi-channel OPMs are utilized to measure the magnetic field at different observation points, where the magnetic fields generated by the OPMs interfere with each other. To suppress the magnetic field interference, this paper proposes a magnetic field compensation method based on an artificial neural network (ANN). The transfer function between the compensation currents and the observed signals is derived, based on which a nonlinear multiparameter optimization problem is derived. Experimental data with different initial magnetic field conditions is collected. Then, an ANN model is employed to optimize the compensation currents of the OPMs to minimize the magnetic field experienced by each sensor. It is demonstrated that this method can effectively reduce the magnetic field crosstalk of multi-channel OPMs.