The image resolution of aerial camera declines resulting from vibration and the dynamic modulation transfer function(MTF) is used to evaluate the impact of vibration on image quality. In accordance with the transfer function theory of linear optical system, a formula based on Bessel function of the first kind is established to calculate dynamic MTF for sinusoidal vibration at any frequency. The tolerance of vibration amplitude is calculated with the restriction that dynamic MTF at Nyquist frequency is no less than 0.9. For low-frequency, the amplitude tolerance declines as frequency rises. And the tolerance of high-frequency is 0.2 pixel. The dynamic imaging experiment of the edge target under sinusoidal vibration is carried out. The experiment shows that the relative error between the MTFs calculated from the derived formula and the MTFs obtained by slanted-edge method from the practical degraded image is less than 4.25%. The accuracy rises 18.5 times compared with other relevant literature. Therefore, the proposed formula can be used to estimate and evaluate the image quality of aerial camera under vibration and is significant for the design of the line-of-sight stabilization system.