The application of pultruded fiber reinforced polymer (FRP) composites in civil engineering is increasing as a high-performance structural element or reinforcing material for rehabilitation purposes. The advantageous aspects of the pultrusion production technique and the weaknesses arising from the 0° fiber orientation in the drawing direction should be considered. In this direction, it is thought that the structural performance of the profiles produced by the pultrusion technique can be increased with 90° windings by using different fiber types. This paper presents experimental studies on the effect of FRP composite wrapping on the flexure performance of reinforced concrete (RC) filled pultruded glass-FRP (GFRP) profile hybrid beams with damage analysis. The hybrid beams are wrapped fully and partially with Glass fiber reinforced polymer (GFRP) and carbon fiber reinforced polymer (CFRP) composites. Hybrid beam specimens with 0° to 90° fiber orientations were tested under three- and four-point bending loads. Based on the experimental load–displacement relationship results, initial stiffness, ductility, and energy dissipation capacity were compared. The experimental findings revealed that the maximum load-carrying capacities of beams produced with pultrude profiles increased by 24% with glass wrapping and 64.4% with carbon wrapping due to the change in the damages. A detailed damage analysis is provided. Similarly, significant increases were observed in structural performance ratios such as initial stiffness and ductility ratio.