This paper develops convergence theory of the gradient projection method by Calamai andMore (Math. Programming, vol. 39, 93-116, 1987) which, for minimizing a continuously differentiable optimization problem min{f .(x): x ∈ Ω} where Ω is a nonempty closed convex set, generates a sequence xk+1=(ak-ak)▽f (xk))where the stepsize ak > 0 is chosen suitably. It is shown that, when f (x) is a pseudo-convex (quasi-convex) function, this method has strong convergence results: either xk→x* and x* is a minimizer (stationary point); or ‖xk‖→arg min{f (x) : x ∈ Ω}= and f (xk) inf{ f (x): x ∈ Ω}.