A new polar and magnetic oxide, LuCrWO6, was synthesized under high pressure (6 GPa) and high temperature (1673 K). LuCrWO6 is isostructural with the previously reported polar YCrWO6 (SG: Pna2(1), no. 33). The ordering of CrO6 and WO6 octahedra in the edge-shared dimers induce the polar structure. The effective size of rare earth, Ln cation does not seem to affect the symmetry of LnCrWO(6). Second harmonic generation measurements of LuCrWO6 confirmed the noncentrosymmetric character and strong piezoelectric domains are observed from piezoresponse force microscopy at room temperature. LuCrWO6 exhibits antiferromagnetic behavior, T-N, of similar to 18 K with a Weiss temperature of -30.7 K.