The rhombohedral perovskite LaAl0.5Ni0.5O3 (or La2AlNiO6), synthesized by a combustion method is found to contain Al3+ and Ni3+ cations in the rhombohedral lattice. The material exhibits a temperature dependent (thermally excited) paramagnetic susceptibility and follows the modified Curie-Weiss law implying an antiferromagnetic ordering at very low temperatures. A non-saturating hysteresis loop with a coercivity of 108 Oe is observed at 2 K which is arising from the magnetic contribution from Ni in the lattice. The conduction mechanism in LaAl0.5Ni0.5O3 for 80-300 K follows the Mott's variable range hopping mechanism. A negative magnetoresistance of 1.75% is observed at 2 K under 90 kOe field which decreases linearly by increasing the temperature up to 18 K and then changes to positive with comparatively low value. Both the negative and positive magnetoresistance increases linearly with an applied magnetic field.