The conformal invariance of a system with unilateral Chetaev non-holonomic is studied, and its definition is given. The relation between the conformal invariance and the Noether symmetry is discussed. Finally, the relation between the conformal invariance and the Lie symmetry is discussed, and the Hojman conserved quantity due to the conformal invariance of the systems is obtained. In the paper, an example is given to illustrate the application of the results.