Non-planar additive manufacturing (AM) demonstrates great potential in enhancing interlayer bonding force and surface smoothness of parts, offering a more flexible design and manufacturing approach for continuous fiber composites to fully exploit material capabilities. This study developed a three-axis printer utilizing an adjustable fiber printing head that can achieve non-planar slicing (NPS) AM of pre-impregnated continuous fibers. The research delves into the influence of deposition inclined angle on the surface roughness of printed samples, enabling the design and printing of NPS samples using continuous carbon fiber (CF), glass fiber (GF), and hybrid fiber composites. The investigation also assesses bending failure morphologies of the printed parts and validates the efficacy of the NPS method through the fabrication of the double-sinusoidal curved surface structure and spherical surface grid structure. The results indicated that maintaining a deposition inclined angle below 15° is crucial to ensure surface accuracy in continuous fiber printed parts. Curved surface bending samples printed with NPS method exhibit substantial enhancements in bending performance and surface accuracy compared to those produced using planar slicing (PS). The NPS-CF sample achieves a remarkable increase of over 170% in maximum bending force and a 63% reduction in surface roughness compared to the PS-CF sample.