In this paper,the Noether symmetry and the Noether inverse the problems of nonholonimic systems with fractional derivatives are studied.Basic on the quasi-invariance of Hamilton action under the infinitesimal group of transformations without the time variable and the general transformations of time-reparametrization,then the fractional Noether theorem of nonholonomic system are established respectively.Further,the fractional Noether inverse problems are firstly presented for the nonholonomic system.An example is designed to illustrate the application of the results.