A nonlinear spring model is proposed to investigate the oscillation behavior of oscillators based on double-walled carbon nanotubes (DWCNTs) with open end by using the finite element (FE) method, where non-linear spring elements are used to represent the van der Waals (vdW) interaction between tubes. Compared to the linear spring FE model, the proposed non-linear springs can more accurately describe the interaction between nanotubes because the vdW interaction is a kind of strongly non-linear force. The influence of boundary conditions, geometric parameters of the DWCNTs, and the layer spacing of tubes on the natural frequencies is especially studied. Various oscillation modes and the corresponding natural frequencies are obtained. Compared to the results obtained by using the linear spring model, the natural frequencies of oscillators based on DWCNTs are in qualitatively better agreement with those obtained from the analytical method and the molecular dynamics (MD) method. From the FE results, it also can be seen that, DWCNTs is expected to be a nanoscale oscillatory device, and its oscillation mode and natural frequency can be adjusted by changing the geometric parameters and boundary condition of the tubes. The proposed nonlinear spring model is helpful for the design of the nano-oscillators under various conditions.