Rolling bearing fault impulses are often submerged in Gaussian and non-Gaussian noise. In addition, multiple faults interfere with each other, making the weak fault not obvious or even difficult to detect. This article proposes a new deconvolution method to solve these two problems—maximum cyclic Gini index deconvolution (MCGID). The method is based on a new index, the cyclic Gini index (CGI), and the classical Gini index (GI) weighting sequence is applied through the fault characteristic frequency and the nearby narrowband range to highlight the amplitude at low order harmonics and weaken the interference components around higher order. This ensures that CGI has the characterization of specific periodic fault impulses and excellent noise robustness. Then, the adaptive filter is designed by maximizing CGI and morphological processing to achieve the detection of the cyclostationary (CS) components associated with the fault impulses. MCGID has a better accuracy than classical methods. Results from simulations and experiments indicate that MCGID performs better at fault impulse detection under severe Gaussian and non-Gaussian interference, and compound fault diagnosis.