This paper focuses on Lagrange symmetries and conserved quantities for nonconservative mechanical systems with nonholonomic constraints of non-Chetaev's type. The definition and criterion of Lagrange symmetry of the systems are given. The conditions under which a Lagrange symmetry can lead to a new conserved quantity（first integral)are obtained and the form of the new conserved quantity（first integral)is presented. Two examples are given to illustrate the application of the results.