Geochemical parameters, e.g., maturity and total organic carbon (TOC) content, play a crucial role in the prediction of sweet spots and the exploration of oil and gas in organic-rich shales. Thermal maturity significantly affects the conversion of solid organic matter into hydrocarbons and the evolution of microstructures, thereby altering the overall elastic properties of shales. To clarify how maturity affects shale properties, we develop a novel rock-physics model (RPM) of organic-rich shale, in which we consider the continuous process of thermal maturity. First, we present how to estimate the maturity level, TOC content, and organic porosity using logging data. Second, different from only considering the discrete-stage maturity, we establish a novel RPM in which a continuous kerogen maturation process serves as a key control condition. Furthermore, we calibrate the volumetric proportion of each porosity type as a function of maturation. Finally, we apply the RPM to investigate how sweet spot parameters (thermal maturity, TOC content, and brittle mineral content), overpressure, and diagenesis affect the overall elastic properties and anisotropy of shale during thermal maturation. Results demonstrate that using our RPM, we may predict the acoustic velocity of shale formations reliably and that kerogen evolution has a noticeable impact on the elastic properties of shale rocks, particularly during the wet gas window stage of mid-to-high maturation. We conclude that thermal maturity emerges as a crucial sweet spot parameter in the case of the exploration of oil and gas in organic-rich shales.