We study the Lie symmetries and Hojman conserved quantities of generalized linear nonholonomic mechanical systems. Under special infinitesimal transformations in which the time is invariable，the determining equations，the constrained restriction equations and the additional restriction equations of the nonholonomic mechanical systems are obtained. The Hojman conserved quantity of the corresponding holonomic systems，the weakly Hojman conserved quantity and the strongly Hojman conserved quantity of the linear nonholonomic systems are obtained. An example to illustrate the application of the result is given.