In this paper we report low-temperature magnetic properties of the rare-earth perovskite material YbAlO3. 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 TN=0.88 K, Yb moments order into the coplanar but noncollinear antiferromagnetic (AFM) structure AxGy, 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 YbAlO3 as a new member of one-dimensional quantum magnets.