Abstract: The Lie symmetry and conserved quantity of relative motion dynamics of nonholonomic systems in phase space on time scales have been studied. Firstly, based on Legendre transformation and Hamilton principle, the Hamilton canonical equation can be established. Secondly, invariance principle based on differential equations under infinitesimal transformation, lie symmetry determination equation and restriction equation can be constructed, the structural equation and the corresponding conserved quantity have been given. Finally, an example is given to illustrate the application of the results.