Abstract: The equivalent source (ES) method in the spherical coordinate system has been widely applied to processing, reduction, field modeling, and geophysical and geological interpretation of satellite magnetic anomaly data. However, the inversion for the ES model suffers from nonuniqueness and instability, which remain unresolved. To mitigate these issues, we introduce both the minimum and flattest models into the model objective function as an alternative regularization approach in the spherical ES method. We first present the methods, then analyze the accuracy of forward calculation and test the proposed ES method in this study by using synthetic data. The experimental results from simulation data indicate that our proposed regularization effectively suppresses the Backus effect and mitigates inversion instability in the low-latitude region. Finally, we apply the proposed method to magnetic anomaly data from China Seismo-Electromagnetic Satellite-1 (CSES-1) and Macau Science Satellite-1 (MSS-1) magnetic measurements over Africa by constructing an ES model of the large-scale lithospheric magnetic field. Compared with existing global lithospheric magnetic field models, our ES model demonstrates good consistency at high altitudes and predicts more stable fields at low altitudes. Furthermore, we derive the reduction to the pole (RTP) magnetic anomaly fields and the apparent susceptibility contrast distribution based on the ES model. The latter correlates well with the regional tectonic framework in Africa and surroundings.