By numerically solving the two-dimensional time-dependent Schr(o)dinger equation under the frozen-nuclei approxi-mation, we are able to study the molecular photoelectron-momentum distribution (MPMD) of H+2 with different orientation angles driven by elliptically polarized laser pulse with varying ellipticities. Our numerical results show that the MPMD is sensitive to the orientation angle and the laser ellipticity, which can be explained by the attosecond perturbation ionization theory and the exactly solvable photoionization model. When the ellipticityε=0, the final MPMD of x-oriented H+2 shows a distinct six-lobe patte that is different from that withε=0.5 andε=1. The evolutions of electron wave packet (EWP) and MPMD with x-oriented H+2 are presented to interpret this distinct patte.