Abstract: To address the problems of insufficient detection depth and limited azimuthal identification capability of instruments for resistivity imaging while drilling in oil-based drilling fluid environments, a multi-frequency azimuthal laterolog resistivity imaging logging structure with plate-type receivers is proposed. Based on the instrument’s operating principle, an equivalent circuit model and a three-dimensional finite element model are established. Model validation is conducted in homogeneous formations. Furthermore, a formation with four azimuthal resistivities, a formation containing high- and low-resistivity anomalies, and an inclined layered formation were constructed to analyze the response characteristics of the real and imaginary parts of impedance at different frequencies and the sensitive range of formation resistivity. The equivalent circuit results show good agreement with the finite element forward modeling results in homogeneous formations. In the four-azimuth formation, the real and imaginary parts at low frequencies exhibited more pronounced responses to variations in high- and low-resistivity layers, while high frequencies can assist in distinguishing different resistive layers. The anomaly model indicates that the response amplitude increases with the enlargement of the azimuthal opening angle, and the real and imaginary parts exhibited complementarity. In the inclined layered formation, multi-frequency joint analysis enhances layer interface identification capability and improve the stability of dip angle calculation. The proposed multi-frequency azimuthal laterolog resistivity imaging scheme effectively characterize azimuthal electrical differences in complex formations, providing a model foundation and methodological reference for imaging logging research under oil-based drilling fluid conditions.