This study had the goal of investigating the effect of the curvature along the heating line on the transverse angular distortion of plates having an initial curvature from line heating. A thermo-elasto-plastic analysis was carried out using 54 models with various radii of curvature, plate thicknesses, and heating speeds. The results show the effect of the curvature along the heating line on the angular distortion in relation to changes in the magnitudes of the curvature, heating speed, and plate thickness. The present numerical results show that the time history of the angular distortion after cooling and reaching the final deformed shape for a plate having an initial curvature is quite different from that of a flat plate. This emphasized the importance of considering the curvature effect on the transverse angular distortion. From the viewpoint of the curvature effect on the deformation, it has been seen that the curvature does not affect the transverse shrinkage. In this study the predicting formula for the transverse angular distortion was derived through a regression analysis. It showed that as the curvature increased, the angular distortion was reduced because of the higher bending rigidity at the same heat input parameter, and the peak points moved toward the origin as the curvature increased.