In this paper the authors present an algorithm for finding a maximum of a pseudo-convex quadratic function over a closed convex set in Euclidean space. They show that some results due to R. Enkhbat and T. Ibaraki [J. Nonlinear Convex Anal. {\bf 4} (2003), no.~1, 43--76; MR1986970] for convex functions can be carried over to pseudo-convex functions as well. The convergence of their proposed algorithm is proven and some numerical examples are presented.