On the assumption that the materials of the pile and the soil around the pile comply with visco-elastic constitutive relation, the partial differential equation governing the axial vibration of piles is first derived. In the case that the viscous characters of materials of the pile and the soil are weak ， the approximate expressions of the nth  order natural frequency and the vibration displacement are obtained with boundary condition of one end fixed and the other free by the multiscale time analysis method. As a result, it is found that: the nth-order natural frequency is the function of damp, stiffness coefficient of soil around pile ； displacement relates to initial displacement, natural frequency, time, pile body position and damp coefficient. In comparison the 4th-order multiscale approximate solution with exact solution, the error between approximate solution and exact solution is very small(only 3%) when damping ratio is less than 0.76. Therefore, under the conditions of higher exponent number and lower damping ratio, multiscale approximate solution is very near to the exact solution, multiscale method can be used for analysing the vibration of viscoelastic pile.