Physically flat but electromagnetic parabolic surface (EPS) is presented. By covering a metal ground plane with periodic metal-dielectric composite textures, the electromagnetic reflection properties can be altered. By tuning the individual lattice of a periodic mushroom-type texture to vary the surface impedance, an EBG surface with a stepped reflection phase as a function of position can be designed. Using a parabolic phase gradient in the reflection coefficient along the face, the surface can be a concave curve inwards in the middle and concentrate a reflected wave. With this technique, an electromagnetic gradient surface on a geometrically flat structure with novel reflection properties can be created. This paper introduces a one-dimensional EPS structure and discusses the reflected beam focusing.