Improving the mechanical properties of 3D printed parts produced through a material extrusion-based 3D printer with continuous fibers (carbon, glass, and aramid) has been a focal point for numerous researchers. Given the layered nature of additive manufacturing (AM) processes, wherein parts are built up layer by layer, most studies involve the deposition of continuous fibers onto a 2D surface. Cases involving curved surfaces have employed robots with high degrees of freedom. This research introduces a method for depositing continuous glass fibers onto curved surfaces, implemented on a cost-effective material extrusion-based 3D printer. The presented approach involves G-code modification, the incorporation of a rotating axis for the nozzle, and the application of computer-aided design and manufacturing techniques. Experimental results affirm the efficacy of this method for depositing continuous fibers onto curved surfaces. The developed technique enables the production of free-form composite shells with a thermoplastic matrix and continuous fiber reinforcement. Lastly, through 3D scanning of the printed sample and subsequent comparison with the 3D model, the degree of surface form deviation and tolerance is determined. The maximum deviation identified in this study is 0.1 mm, a tolerable amount considering the inherent characteristics and behaviors of thermoplastic materials (shrinkage and warpage) during production processes.