The author considers the constrained minimization problem \[ \text{minimize}\quad f(x)\quad\text{subject to the simple bounds}\quad \ell\leq x\leq u, \] where \(\ell\), \(u\) are two fixed points, and \(f: \mathbb{R}^n\to \mathbb{R}\) is a Lipschitz continuously differentiable function. An extension of his conjugate gradient algorithm [IMA J. Numer. Anal. 14, No. 3, 443-460 (1994; Zbl 0830.65052)] is given. He proves convergence properties of the proposed algorithm. Numerical results of applying this algorithm to large-scale test problems (with more that 10,000 variables) are also presented.