Continuous fiber-reinforced thermoplastic composites (CFRTPCs) have advantages such as high specific strength, high specific modulus, corrosion resistance, and recyclability and are widely used in the fields of aerospace, rail transit, new energy, and so on. However, traditional methods for preparing CFRTPCs, such as placement and molding, rely more on forming molds, resulting in high manufacturing costs and a slow response speed, which limits the promotion and application of the new generation of CFRTPCs with complex configurations and designable performance. Three-dimensional printing can efficiently create products with multiple materials, complex structures, and integrated functions, introducing new ways and opportunities for the manufacturing of CFRTPCs. However, poor mechanical properties are the bottleneck problem in achieving 3D printing of CFRTPCs. This paper summarizes the research status of the fused deposition modeling (FDM) 3D printing process and the corresponding mechanical properties of CFRTPCs. The focus is on analyzing the influences of the FDM process parameters, such as the material type, printing temperature, speed parameters, layer thickness, scanning space, stacking direction, and fiber volume content, on the mechanical properties of CFRTPCs. Finally, the main problems and future prospects of current CFRTPCs-FDM are analyzed and forecasted, providing new references and ideas for 3D printing of high-performance CFRTPCs.