In this paper, a coaxial extrusion-based additive manufacturing process has been developed for three-dimensional (3D) printing of continuous carbon fiber reinforced thermoplastic composites. A special coaxial nozzle was developed to feed continuous carbon fiber and thermoplastic pellets and extrude layer-by-layer to manufacture three-dimensional (3D) composite parts. To have continuous deposition, a computational algorithm has also been developed to optimize extrusion path planning for continuous fibers with thermoplastic materials with no- or minimum stop. The results from the mechanical tests showed that continuous carbon fiber reinforced composite materials resulted in higher tensile and flexure test values than pure thermoplastic materials.