The effects of spatialcurvature radius on the laser cutting quality indexes of pipe with spiral cutting patternsuch as the top kerf width, the extent of heat-affected zone (HAZ), the cut surfaceroughness Rz, the microhardness (HV0.1), the half-squareness were investigated.The results show that the values of the kerf width on the upper surface, thehalf-squareness, and the HAZ increase with the increase of spatial curvature radius exceptfor the values of the cut surface roughness Rz as the diameter of pipe remains unchangedand the pitch increases. The main reason is the heat accumulation and preheating effects.