We will argue that the 1/2 BPS Wilson loops in the anti-symmetric representations in the N = 4 super Yang-Mills (SYM) theory exhibit a phase transition at some critical value of the 't Hooft coupling of order N-2. In the matrix model computation of Wilson loop expectation values, this phase transition corresponds to the transition between the one-cut phase and the two-cut phase. It turns out that the one-cut phase is smoothly connected to the small 't Hooft coupling regime and the 1/N corrections of Wilson loops in this phase can be systematically computed from the topological recursion in the Gaussian matrix model.