Seismic impedance inversion has become a common approach in reservoir prediction. At present, the critical issue in the application of seismic inversion is its low computational efficiency, especially in 3D. To improve the computational efficiency, we have developed an inversion method derived from the proximal objective function optimization algorithm. Our inversion method calculates each unknown parameter in the model vector, one by one during iteration. Compared with routine gradient-dependent inversion algorithms, such as the iteratively reweighted least-squares (IRLS) algorithm, our inversion method has lower computational complexity as well as higher efficiency. In addition, to obtain a sparse reflectivity series, a long-tailed Cauchy distribution is used as the a priori constraint. The weak nonlinear problem owing to the introduction of Cauchy sparse constraint is addressed by taking advantage of reweighting strategy. Results of synthetic and real data tests illustrate that the proposed inversion method has higher computational efficiency than IRLS algorithm, and its inversion accuracy remains the same.