A theoretical study has been undertaken to determine the flow characteristics associated with a three-dimensional laminar impinging jet issuing from a square pipe nozzle. Interesting flow structures around the jet are detected. The numerical result reveals the existence of four streamwise velocity off-center peaks near the impingement plate, which is different from the rectangular jet impingement. The mechanism of the formation of the off-center velocity peaks and the parameters affecting the flow-field characteristics are discussed by comparison of the computed results with different nozzle-to-plate spacings and Reynolds numbers.