The paper studies the nonlinear vibrating mechanical behaviors of double-walled carbon nanotubes (DWCNTs) with the initial axial stress under the temperature field. The DWCNTs are modeled as double elastic shells coupled together through vdW interaction between inner and outer nanotubes. Based on the model, the relation between the amplitudes and the frequencies of the tubes is achieved. The results show that the initial axial stress could crucially affect the topological forms of the amplitude-frequency curve, whereas it is insensitive to the amplitude ratios in DWCNTs. Meanwhile, it is also concluded that the temperature change is significant for natural frequency, but weakly affects intertube frequency and amplitude ratios as well as amplitude-frequency curve.