Estimating the total organic carbon (TOC) content is crucial in shale reservoir evaluation. Among the available methods for TOC estimation from well logs, the ΔlogR technique is currently the only globally used model that is based on a rigorous petrophysical model. Literature reviews reveal that the overlay-coefficient between the porosity and the resistivity curves in the ΔlogR model has been the focus of many studies. However, the current methods of determining the overlay-coefficient based on the rock minerals or empirical parameters weaken its applicability and accuracy. In this study, we developed a V-ΔlogR model for the prediction of the total organic matter content. The V-ΔlogR model is comprised of three modifications to the ΔlogR model, i.e., replacing the fixed overlay-coefficient with a variable one, removing the maturity, and replacing the baselines with a single one. Among these, a critical improvement is treating the overlay-coefficient ( k ) as a variable and determining it from the measured TOC values or from well logs. The application of our improved model in the Songliao, Bohai Bay, and Sichuan basins indicates that the V-ΔlogR model can accurately predict the TOC of shale with large lithological and mature variations. Because it uses actual geological data to determine the overlay-coefficient in the model, the V-ΔlogR model offers more reliable results for test wells than other commonly used models (e.g., the modified Schomoker, multiple regression analysis, modified ΔlogR). The V-ΔlogR model eliminates the need for mineral and maturity data constraints and the overlay-coefficient can be determined using only the well logs, which significantly expands the applicability of the ΔlogR method. • An improved method (the V-ΔlogR model) predicts TOC content is proposed. • The method is based on sonic and the resistivity log, and a ratio of k between them. • A easily implemented method for predicting k using the log curves is presented. • The V-ΔlogR model expands the applicability of the ΔlogR method, and can be accurate in TOC predicting.