Usually, many people work for solving convex minmization problems with various constraints, including some fuzzy conditions. In this paper, we present some algorithms for solving quadratic maximization problems with some fuzzy constraints. The objective function of the encountered problem is quadratic with a feasible region of a reverse convex constraint. Even without fuzzy nature, the problem still remains in the category of NP-hardness, which can be solved in typical global optmization. We transform the reverse convex feasible region to a d.c. (difference of convex) set, then solve the problem in combining the techniques of d.c. method and on-line vertices enumeration method.