The changing element size or numbers are always introduced in the traditional FEM, which is not suitable for programming and cannot ensure the computational accuracy. Based on the generalized moving least squares (GMLS), an improved global interpolating element-free Galerkin (EFG) method was applied to dynamics of an axially deploying or retracting flexible beam. The element-free transverse vibration equations were built according to the Hamilton principle. The frequency characteristics，free vibration with different axially motion and the forced vibration response of the beam are calculated in numerical examples. By comparing with the reported available results, the feasibility of the EFG method applied for the time-varying parameter systems is verified.