We study a Liouville type theorem for stable solutions of the followingsemilinear equation involving Grushin operators xu a2x2αyuup1u, x, yRN RN1RN2where p >
1, α >
0 and a 6= 0. Basing on thetechnique of Farina [1], we establish the nonexistence of nontrivial stable solutionsunder the range p cNαwhere Nα N1 +(1+αN2, and pcNαis a certain(explicitly given) positive constant depending on Nα