The low-thrust capture orbit design is considered by analyzing the maximum hyperbolic excess velocity that can realize the capture with constrained thrust magnitude and given semi-major axis of the target elliptical capture orbit. The optimal control problem is formulated and transformed into a two-point boundary value problem by the indirect method. The characteristics of costate variables are analyzed to obtain two-dimensional nonlinear equations, where the eccentricity and true anomaly of the target elliptical orbit are identified as the independent variables. As for the Mars capture, the maximum hyperbolic excess velocity increases when the maximum thrust acceleration, capture time, and semi-major axis become larger. The minimum and maximum capture times are revealed, and the corresponding optimal control laws and multi-revolution capture trajectories are presented. Finally, the application of the maximum hyperbolic excess velocity analysis is discussed, and possible future research is summarized.