In this paper we report low-temperature magnetic properties of the rare-earth perovskite material YbAlO 3 . Results of elastic and inelastic neutron scattering experiment, magnetization measurements along with the crystalline electrical field (CEF) calculations suggest that the ground state of Yb moments is a strongly anisotropic Kramers doublet, and the moments are confined in the ab-plane, pointing at an angle of ϕ = ±23.5 • to the a-axis. With temperature decreasing below T N = 0.88 K, Yb moments order into the coplanar, but non-collinear antiferromagnetic (AFM) structure Ax G y, where the moments are pointed along their easy-axes. In addition, we highlight the importance of the dipole-dipole interaction, which selects the type of magnetic ordering and may be crucial for understanding magnetic properties of other rare-earth orthorhombic perovskites. Further analysis of the broad diffuse neutron scattering shows that one-dimensional interaction along the c-axis is dominant, and suggests YbAlO 3 as a new member of one dimensional quantum magnets.