Abstract: The Lie symmetry and the Mei symmetry for dynamical systems with non-standard Lagrangians have been presented and studied.By introducing the infinitesimal transformations and their generating vectors,and in light of the Lagrange equations of the systems,the definitions of Lie symmetry and Mei symmetry have been given,and the structure equations of Lie symmetry and Mei symmetry for two types of dynamical systems with non-standard Lagrangians (i.e.with exponential Lagrangians and power-law Lagrangians) have been established.The Noether conserved quantity resulted from Lie symmetry and the Mei conserved quantity resulted from Mei symmetry have been derived.In addition four examples have been given to illustrate the application of the results.