Image dehazing, a crucial task in low-level vision, supports numerous practical applications, such as autonomous driving, remote sensing, and surveillance. This paper proposes IHDCP, a novel Inverted Haze Density Correction Prior for efficient single image dehazing. It is observed that the medium transmission can be effectively modeled from the inverted haze density map using correction functions with various gamma coefficients. Based on this observation, a pixel-wise gamma correction coefficient is introduced to formulate the transmission as a function of the inverted haze density map. To estimate the transmission, IHDCP is first incorporated into the classic atmospheric scattering model (ASM), leading to a transcendental equation that is subsequently simplified to a quadratic form with a single unknown parameter using the Taylor expansion. Then, boundary constraints are designed to estimate this model parameter, and the gamma correction coefficient map is derived via the Vieta theorem. Finally, the haze-free result is recovered through ASM inversion. Experimental results on diverse synthetic and real-world datasets verify that our algorithm not only provides visually appealing dehazing performance with high computational efficiency, but also outperforms several state-of-the-art dehazing approaches in both subjective and objective evaluations. Moreover, our IHDCP generalizes well to various types of degraded scenes. Our code is available at https://github.com/TaoLi-TL/IHDCP.