Using mainly numerical methods, we investigate the width of the spin gap of a spin-1/2 two-leg ladder described by equation image, where equation image denotes the α-component of the spin-1/2 operator at the j-th site of the a (b) chain. We mainly focus on the equation image ≫ equation image and equation image case. The width of the spin gap between the M = 0 and 1 subspaces (M is the total magnetization) as a function of λ anomalously increases near λ = 0; for instance, for equation image ≲ equation image ≲ equation image when Jl/Jr = 0.1. The gap formation mechanism is thought to be different for the λ < 0 and λ > 0 cases. Since, in usual cases, the width of the gap becomes zero or small at the point where the gap formation mechanism changes, the above gap-increasing phenomenon in the present case is anomalous. We explain the origin of this anomalous phenomenon by use of the degenerate perturbation theory. We also draw the ground-state phase diagram.