Summary: This paper develops convergence theory of the gradient projection method by P. H. Calamai and J. J. Moré [Math. Program. 39, 93-116 (1987; Zbl 0634.90064)] which, for minimizing a continuously differentiable optimization problem \(\min \{f(x): x\in \Omega\}\) where \(\Omega\) is a nonempty closed convex set, generates a sequence \(x_{k+1}= P(x_k- \alpha_k \nabla f(x_k))\) where the stepsize \(\alpha_k> 0\) is chosen suitably. It is shown that, when \(f(x)\) is a pseudo-convex (quasi-convex) function, this method has strong convergence results: either \(x_k\to x^*\) and \(x^*\) is a minimizer (stationary point); or \(\|x_k\|\to \infty\), \(\arg\min \{f(x): x\in \Omega\}= \emptyset\), and \(f(x_k) \downarrow \inf\{f(x): x\in \Omega\}\).