We look at the strong field behavior of the Wang-Yau quasi-local energy. In particular, we examine the limit of the Wang-Yau quasi-local energy as the defining spacelike 2-surface approaches an apparent horizon from outside. Assuming that coordinate functions of the isometric embedding are bounded in and mean curvature vector of the image surface remains spacelike, we find that the limit falls in two exclusive cases: 1) If the horizon cannot be isometrically embedded into , the Wang-Yau quasi-local energy blows up as   approaches the horizon while the optimal embedding equation is not solvable for   near the horizon; 2) If the horizon can be isometrically embedded into , the optimal embedding equation is solvable up to the horizon with the unique solution at the horizon corresponding to isometric embedding into  and the Wang-Yau quasi-local mass admits a finite limit at the horizon. We discuss the implications of our results in the conclusion section.