A hybrid many-body-expansion/Shepard-interpolation method for constructing globally accurate potential energy surfaces (PESs) is presented. Incorporation of the many-body expansion strategy into the conventional Shepard interpolation method, greatly reduced the configuration space need to be interpolated, and furthermore, all the asymptotic channels can be represented accurately. A total of 30 "ab initio" points (taking LSTH PES as the source of pseudo ab inito calculations) are found to be sufficient for constructing chemically accurate H-3 PES appropriate for uses in dynamics calculations. The excellence of the constructed PES is demonstrated by accurate quantum dynamics calculations. (C) 2012 Elsevier B. V. All rights reserved.