In this study, the surface was constructed using Frenet vectors along a curve known as T-pedal curve, which is geometric location of the perpendicular projection points from a point not on the curve onto the tangent vector of any curve. Then surfaces containing the T-pedal curve were characterized using marching-scale functions by employing Frenet vectors along the T-pedal curve. Finally, the geometric properties, Gaussian and Mean curvatures of these obtained surfaces are calculated.