The supercritical flow depth at the bucket of the outlet structures is an important parameter for flow connection in the downstream of outlet work, design of bucket radius and dynamic water pressure calculation. The aim of this paper is to seek a calculation method of supercritical flow depth at the bucket of the outlet structures with sufficient accuracy and convenient calculation. Based on the analysis of the supercritical flow at the bucket of the outlet structures using the energy equation of the rapidly varied steady flow, the water depth equation of the bucket derived by the energy equation of the rapidly varied steady flow was approximated by series expansion, and the explicit solution of the supercritical flow depth at the bucket of the outlet structures was obtained. Error analysis of exact solution and explicit solution showed that the error of the supercritical flow depth at the bucket decreases with the increase of the velocity coefficient when the velocity coefficient of the rapidly varied flow varied from 0.85 to 1.0. The error of the supercritical flow depth at the bucket decreased with the decrease of the flow-energy ratio when the flow-energy ratio varied from 0.01 to 0.3. The maximum error of the proposed formula was less than 1.85%. It can be seen that the explicit solution of the supercritical flow depth at the bucket of the outlet structures proposed in this paper is simple, convenient, and accurate in the range of the parameters of the actual project. Therefore, it can be applied to the hydraulic calculation of the supercritical flow depth at the bucket of the outlet structures in practical engineering.