High-speed 3D printing has recently gained much interest due to its potentials in improving efficiency of fabricating complex geometry components and applications in large-scale additive manufacturing (AM). In this study, a parametric study is performed experimentally to investigate factors affecting high-speed 3D printing of continuous carbon fiber reinforced composites (CFRCs), including material deposition rate, print (nozzle traverse) speed, and nozzle tilt angle based on a novel multi-axis AM approach. The method uses thermoplastic pellets and continuous carbon fiber tows as feedstock materials. The obtained sample quality and mechanical properties are investigated with respect to deposition rate, print speed, and nozzle tilt angle. The fiber impregnation quality is examined through microstructure analysis and correlated with the process conditions and mechanical properties. Increasing deposition rate and tilt angle both improve fiber impregnation quality, enabling implementation of higher print speed and yielding improved mechanical properties. This, combined with demonstrations of printed complex geometry components, shows the great potentials of the proposed method for AM of continuous CFRCs at high speeds. The results of this study also provide further guidance on design and manufacturing of large-volume, high-strength CFRCs through 3D printing.