The magnetic ordering of alpha-U3O8 remains a puzzling question for a long time. Recent inelastic neutron scattering study exhibited magnetic peaks at (0.5,1,1) and (0.5,2,2) but without intensity at (0.5,0,0). The magnetic propagation vector could still be k = (0.5,0,0), as the probability that the magnetic moments are perpendicular to the reflection plane (0.5,0,0) leading to zero intensity should be not ruled out. Magnetic symmetry analysis leads to 4 distinct magnetic structures, and the first-principles calculations show that the possible ground state of U3O8 could be collinear antiferromagnetic (AFM) ordering (m divide divide a-axis). Only one paramagnetic-AFM phase transition at T (1) = 24 K in magnetization curves has been confirmed, which shifts to lower temperatures as the magnetic field increases. At T = 1.8 K, no hysteresis loop around zero field has been observed which could exclude ferromagnetic ground state in this compound. Neutron powder diffraction data have been collected at several temperatures (300, 40, 15 and 5 K), and the absence of visible magnetic reflections makes the unusual magnetic properties even more mysterious.