A non-Noether conserved quantity, i.e. Hojman conserved quantity, of the nonholonomic mechanical systems is presented. Using the special Lie symmetry under infinitesimal transformations in which the time is not variable, the determining equations, the constrained restriction equations and the additional restriction equations of the nonholonomic mechanical systems are given. The Hojman conserved quantity of the corresponding holonomic systems, the weakly Hojman conserved quantity and the strongly Hojman conserved quantity of the nonholonomic systems are obtained. An example is given to illustrate the application of the result.