In this paper, direct numerical simulation of fully developed turbulent pipe flow is carried out at Reτ ≈ 170 and 500 to investigate the effect of the streamwise periodic length on the convergence of turbulence statistics. Mean flow, turbulence intensities, correlations, and energy spectra were computed. The findings show that in the near-wall region (below the buffer region, r+ ≤ 30), the required pipe length for all turbulence statistics to converge needs to be at least a viscous length of O(6300) wall units and should not be scaled with the pipe radius (δ). It was also found for convergence of turbulence statistics at the outer region that the pipe length has to be scaled with pipe radius and a proposed pipe length of 8πδ seems sufficient for the Reynolds numbers considered in this study.