The present invention relates to a system for a parabolic solar concentrator (SCA) having a substantially continuous reflective surface aiming to maximize the efficiency of the parabolic solar concentrator and of its fabrication method. The system of the present invention allows the fabrication of a low cost parabolic solar concentrator, based on a torsion bar, ribs and a plurality of reflective pieces of sheet metal preferably covered with a reflective film. The parabolic solar concentrator according to a preferred embodiment allows the reduction of surfaces shading the reflective surface. Another advantage is the lack of presence of supporting or movement elements protruding in the concave side of the parabola, not including receiver tube components and supports, thereby increasing the reflection efficiency and solar collection.