Rock-physics inversion has been widely used in reservoir prediction. However, the prediction and evaluation of source rocks still predominantly rely on data-driven inversion methods. To directly incorporate the rock-physics relationship into the seismic inversion of source rocks, we first introduce a linearization approximation of the rock-physics model through the first-order approximation of the Taylor series. Model examples and well-logging tests substantiate the reliability of this linear approximation in establishing the connection between the elastic moduli and essential physical parameters (EPPs) of source rocks. Subsequently, we develop a novel equation for the P-wave reflection coefficient by combining the linear rock-physics relationship and Gray approximation. The newly developed reflectivity equation is a linear expression of differences in EPPs of source rocks. Model-simulating results demonstrate a favorable agreement between the novel P-wave reflectivity equation and the exact Zoeppritz equation until the incident angle reaches 60°. Furthermore, we explore the amplitude-variation-with-angle (AVA) effects of EPPs to validate their contributions meet the requirement of seismic inversion. Under the Bayesian scheme, we further develop an AVA inversion method, based on the novel P-wave reflectivity equation, to predict the EPPs of source rocks. Our AVA inversion method obtains satisfactory results under noise testing and demonstrates promising application potential in field examples. The predicted EPPs indicate a strong agreement with the actual well loggings. Comparative analysis against data-driven inversion results reveals that the EPPs predicted by our AVA inversion method possess enhanced rock-physics support and significance. Specifically, this study focuses on isotropic clay-rich source rocks with low maturity.