In this paper, the effect of the coil structure, as well as the gas pressure, on the spatial distribution of an inductively coupled argon plasma is numerically investigated based on our developed three-dimensional fluid model. The model is based on a modified ambipolar diffusion model, in which the electron density is solved under the quasi-neutral condition, the ion density and neutral particle density are obtained by solving continuity equations, and the ion flux is achieved by solving the full momentum balance equation. In addition, the inductive electric field is governed by the Maxwell equations, which are solved in the frequency domain. The results show that the electron density is nonuniform along the azimuthal direction due to the asymmetry of the coil structure, and the uniformity becomes better as gas pressure decreases. Besides, the plasma azimuthal uniformity can also be improved by reducing the opening of the coil. As the coil radius increases, the plasma density decreases, while the radial uniformity of the plasma improves, and the azimuthal uniformity deteriorates. In addition, the influence of the current amplitude ratio between the inner coil and outer coil on the plasma uniformity in dual-coil discharge is also investigated. It is found that the plasma radial uniformity becomes better by reducing the inter-to-outer coil current amplitude ratio. The results obtained in this work demonstrate that the plasma uniformity can be improved by optimizing the coil structure and adjusting the discharge parameters, which is of significant importance in etching and deposition processes.