To study the variation of the damp coefficients of a slender body during water exit, the vibration theory of an elastic body and the potential flow theory of fluid are adopted. For viscous damp coefficient, vortex induced vibration (VIV) model is introduced and the lift and drag forces are included in the structure vibration equation. The increment of damp coefficient by VIV is therefore obtained. For wave-making damp coefficient, time-domain Green Function is adopted. The problem of a sphere oscillating on the free surface is calculated first and compared with the published paper, and the results agree well with each other, which validates the numerical model and procedure in this paper. Based on this, the wave-making damp coefficient of a slender body under different vibration frequencies and different lengths during water exit are calculated and analyzed. The results show that the increment of damp coefficient by VIV rises with the increase of current, wave and the reduction of cavitation, while the wave-making damp coefficient is closely related to the length of water exit, the natural vibration mode and the vibration frequency of the slender body. For the case studied in this paper, the wave-making damp coefficient peaks when the head of the body comes out of the water and the vibration frequency is around 0.5 Hz, and the wave-making damp coefficient induced by the first and second order elastic vibration respectively is quite small, which can be neglected in the engineering application.