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 \(\Sigma\) approaches an apparent horizon from outside. Assuming that coordinate functions of the isometric embedding are bounded in \(W^{2,1} \)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 \(R^3 \) , the Wang-Yau quasi-local energy blows up as \(\Sigma\)  approaches the horizon while the optimal embedding equation is not solvable for \(\Sigma\)  near the horizon; 2) If the horizon can be isometrically embedded into \(R^3 \), the optimal embedding equation is solvable up to the horizon with the unique solution at the horizon corresponding to isometric embedding into  \(R^3 \) 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.