The turbulent structure of oscillating pipe flow was investigated by direct numerical simulation. And the mechanism of interaction between the turbulent structure and the imposed oscillations was also studied. Spectral method was applied to calculation of the velocity field, which was represented using Fourier series in the streamwise and spanwise directions, and Chebyshev polynomial series in the normal direction. The numerical results at Re=8500 and Re=72100 were discussed about the wall shear stress and turbulent statistics.