The operational system of the spacecraft is general a variable mass one, of which the symmetry and the conserved quantity imply physical rules of the space system. In this paper, Tznoff equations of the variable mass nonholonomic system are derived, from which the Lie symmetries of Tznoff equations for the variable mass nonholonomic system and conserved quantities are derived and are researched. The function expressions of conserved quantities and the criterion equations which deduce these conserved quantities are presented. This result has some theoretical value for further research of the conservation laws obeyed by the variable mass system.