Noether symmetry and Noether conserved quantity of Nielsen equation in a dynamical system of the relative motion with nonholonomic constraint of Chetaev's type are studied. The differential equation of motion of Nielsen equation for the system, the definition and the criterion of Noether symmetry, and the expression of Noether conserved quantity deduced directly from Noether symmetry for the system are obtained. An example is given to illustrate the application of the results.