The Earth’s magnetic field, which has been extensively observed from ground to satellite altitudes over several decades, originates from multiple sources, such as the core dynamo, the conductive mantle, the magnetized lithosphere, and the space current systems. Modeling of the lithospheric contribution plays an important role in the geophysical studies and industrial applications. In this paper, we propose a new method for global and regional modeling of the lithospheric magnetic field based on the cubed-sphere. An equivalent dipole source method on a quasi-uniform cubed-sphere grid is employed in the forward modeling. The dipole directions are fixed according to a priori magnetization and the relative intensities are estimated by an inversion procedure of least-squares fitting with minimum model regularization. Several numerical tests are performed to validate the accuracy and efficiency of both forward modeling and inversion procedure. The proposed method is applied to the global and regional modeling based on the latest magnetic data from Swarm Alpha satellite and MSS-1 mission. The model results indicate that the proposed method works quite well for realistic satellite data and MSS-1 data is consistent with the Swarm data in terms of lithospheric field modeling.