An accurate potential energy surface of the He-H-2 interaction is calculated with a large basis set at the complete fourth-order Moller-Plesset approximation. The basis set-a combination of a nucleus-centered set 6s4p2d and a bond function set 3s3p2d centered at the midpoint between He and the H-2 center of mass-is designed to give the optimal description of both the intra-and intersystem correlation effects. The validity of the basis set is confirmed by extensive preliminary calculations on the linear (orientation angle theta=0-degrees), bent (45-degrees), and T-shaped (90-degrees) structures at a fixed separation (R=6.5a0) with a series of large basis sets containing different polarization functions and/or bond functions. Bond functions are found more effective than polarization functions in recovering the intersystem correlation energy and they are particularly useful in removing the geometric bias of a basis to give an accurate description for the potential anisotropy and the relative energies of different structures. The effect of bond functions is insensitive to the displacement of bond functions and the geometric midpoint of the van def Waals bond is a satisfactory choice for the center of bond functions. The potential energy surface of He-H-2 is calculated at 15 values of R from 2.0 to 15.0a0 along each of the three main configurations (theta=0-degrees, 45-degrees, and 90-degrees) with the vibrationally averaged H-2 bond length r=1.449a0. Additional calculations are given for r=1.28 and 1.618a0 to show the effect of H-2 zero-point vibration. While our potential at the self-consistent field (SCF) level is essentially the same as the previous calculations, our potential at the correlated level is globally deeper in the attractive region and less repulsive in the shorter range. Our calculated well depth (47.19 muhartrees) corresponding to the global minimum at theta=0-degrees and R=6.5a0, is very close to the estimated experimental value of 48 muhartrees. In the Legendre expansion, our potential compares very well with the empirical potential of Rodwell and Scoles, but differs considerably from the empirical potential of Tang and Toennies and the previous ab initio potentials.