The hydro unit-commitment (HUC) problem aims to determine the status of generating units (GUs) and their generation levels, usually in a day-head planning horizon. The HUC is a complex mixed-integer nonlinear programming (MINLP) problem whose great challenge is accurately representing each hydro production function (HPF) with high computational efficiency. This work proposes to solve the HUC problem using an algorithm based on mixed-integer linear programming (MILP) that updates the gross head iteratively and splits the univariate HPF into concave and convex regions. Piecewise linear approximations are created via the convex hull for concave regions, allowing gathering identical UGs to alleviate the computational burden. On the other hand, the multiple choice model approximates the HPF convex regions. The simulations, carried out in two cascade systems, one with five plants and 18 GUs and the other with four plants and 53 GUs, show that the proposed approach can solve the problem quickly and accurately.