A three-parameter pair-potential model recently constructed is improved in the short-and long-range interaction regions. We demonstrate that this improved potential function is able to accurately describe the entire potentials of the ground-state van der Waals systems such as rare-gas, triplet H-2, Alkalihelium, Alkaline-earth, and group 12 diatomic systems. All these systems show a single binding-energy relation in the attractive region. The improved function suggests a unique form for describing the potentials of diatomic systems ranging from strongly-bound to weakly-bound diatomic systems. (C) 2014 Elsevier B. V. All rights reserved.