Abstract: Using the Lie symmetry under infinitesimal transformations in which the time is not variable,the Hojman's conservation theorems for Raitzin's canonical equations of nonholonomic systems of non-Chetaev's type are studied.The differential equations of the systems and the determining equations of Lie symmetry under infinitesimal transformations are given.The Hojman's conservation theorems of the systems are established.Finally,we give an example to illustrate the application of the result.