To further reveal the inner relationship between the symmetry and the conserved quantity for a dynamical system, the Lie symmetry and the conserved quantity for a non-conservative Hamilton system based on fractional model are proposed and studied. Firstly, the fractional Hamilton canonical equations are established based on the fractional Hamilton principle for the non-conservative system. Secondly, the determining equations under the infinitesimal transformations of a group are given, and the definition of the Lie symmetry for the non-conservative Hamilton system under fractional model is established. The condition under which a Lie symmetry can lead to a new type of fractional Noether conserved quantity is gained and the form of the conserved quantity is presented. Finally, an example is given to illustrate the application of the results.
