Abstract: Helicoidal surface is a surface formed by a plane curve that rotates around a fixed axis while uniformly shifting along the direction of the axis. Helicoidal surface can be divided into elliptic， hyperbolic and parabolic types based on different rotation axis. The helicoidal surface of parabolic type is studied by using Blaschke metric in affine spaces. The helicoidal surfaces of parabolic type whose Gaussian curvature and mean curvature vanish identically have been classified， respectively. When h=0， the helical motion degrades into rotational motion. In this situation， the flat and minimal parabolic surfaces of revolution are also classified. Finally， some graphs of those surfaces are given.

Key words: affine space, parabolic helicoidal surface, flat, Blaschke metric, minimal surface