Abstract: The helicon plasma exhibits the advantages of a high rate of ionization, high density and low confinement magnetic field. It has been widely used in plasma thruster, semiconductor etching, etc. The density of helicon plasmas would be monotonically dependent on the external magnetic field when the magnetic field intensity is sufficiently strong. However, it does not hold at low magnetic fields, which are characterized by a density peak (or low-field peaks). In this paper, a three-dimensional numerical model of argon helicon plasma discharge was established based on the detailed consideration of particle collision and chemical reaction. The characteristics of low-field peaks under different three-dimensional non-uniform magnetic field distributions were simulated and analyzed. The main simulation results show that there are density peaks with the increase of the maximum magnetic field intensity within a certain magnetic field range. Below a threshold (B_max<120 G), the power deposition caused by Doppler-shifted cyclotron damping and anomalous Doppler damping is dominant when the low field peak occurs, and the power deposition peak is distributed near the standing helicon wave. Above the threshold (B_max≥120 G), the power deposition caused by collision damping is dominant. The distribution of power deposition caused by Landau damping and collision damping is close, mainly at the plasma edge and end plate. The left-hand polarization electric field component and right-hand polarization electric field component of the helicon wave propagate in the plasma simultaneously. By changing the magnetic field distribution, the amplitude of the polarization electric field component of helicon wave, propagation properties (traveling wave, standing wave, and partially travelling-partially standing wave), power deposition, density and temperature distribution can be controlled when the low field peak is generated. The standing wave and power deposition generated by helicon wave are mainly distributed in the region with high magnetic field. The relevant research results may provide certain theoretical guidance for revealing low-field peak mechanism of helicon wave plasma.