The self-sustaining turbulent flow in a straight square duct is simulated using direct numerical simulation (DNS). The underlying flow dynamics in a square duct is numerically investigated by using the three-dimensional proper orthogonal decomposition (POD) technique. The method of snapshot POD is an efficient tool to educe coherent structures from the fluctuating component of the DNS database at frictional Reynolds number of 300 (based on duct width and frictional velocity). The coherent structures are manifested through the spatial analysis of POD modes. The spatial POD modes depict the first two most energetic modes as streamwise-independent rolls (or non-propagating modes). The third and fourth most energetic mode are observed as streamwise-dependent structure (or propagating modes). The higher POD modes demonstrate the loop-like structure near the wall region and detached structures in the wake region of the square duct.