This paper applies the Radial Basis function (RBF) collocation method to compute the eddy current magnetic field coupled with conductor movement. Because of the linear characteristic of the RBF collocation matrix equation, the unknown magnetic vector potential could be easily decoupled and directly expressed in moving coordinate systems without model recast. This offers a great convenience to deal with the conductor movement. Time-domain iteration is constructed to solve the governing equations. And in each iteration step, the magnetic field and kinetic equations are calculated alternately. Two numerical examples, the TEAM workshop problem 28 and a transient coil gun problem are considered to analyze the accuracy and efficiency of this method.