Accurate non-Bo-Oppenheimer variational calculations of all bound states of the positive muon molecular ion 4Heμ+have been performed using explicitly correlated Gaussian functions in conjunction with the global vectors. All the energies obtained are accurate in the order of 10-6 Hartree (1 Hartree=27.2114 eV). Compared with the binding energies obtained from calculations based on the Bo-Oppenheimer potential with the mass-weighted adiabatic corrections (Chem. Phys. Lett. 110487 (1984)), the largest relative deviation is up to 15％. By analyzing the average interparticle distances and possibility distributions of interparticle distances of this system, it is confirmed that the Bo-Oppenheimer approximation is reasonable for this system and that 4Heμ+ can be regarded as a system of positive muon bound to a slightly distorted helium atom.