The process of filling-up high-pressure gas storage vessels consists of a gas source tank, an isenthalpic (Joule-Thomson or J-T) valve, a cooling system, and a gas storage vessel. These units are assumed to be thermally insulated. The fill-up process is formulated as a minimum time optimal control problem. Despite the nonlinear nature of the aforementioned optimal control problem, its global solution is obtained analytically. A novel transformation technique is employed, to decompose the problem into a process simulation problem independent of time, and a simpler minimum time control problem that only depends on the final molar density value and the maximum allowable feed mass flowrate. The feasibility of the fill-up is uniquely determined by the process simulation problem, and upon fill-up feasibility, the minimum time control problem is then globally solved. Two fill-up case studies, involving two different system configurations are analyzed. In Case 1, the fill-up process has a constant molar enthalpy feed, and no cooling system. Case 2 considers a fill-up process with a constant temperature feed, delivered by an efficient cooling system. It was demonstrated that the optimal control strategy to achieve minimum fill-up time is to have the mass flowrate at its maximum allowable value during the entire duration of the fill-up. The presented problem formulation is general and can be applied to the fill-up of other gases, such as compressed natural gas. Copyright (C) 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.