Sandwich panel structures have widespread applications in various components, owing to their excellent lightweight properties. However, conventional manufacturing methods involve multiple steps, which limits the exploration of innovative sandwich panel structure. In this study, an integrated 3D printing method for continuous fibers reinforced sandwich panel with Triply Periodic Minimal Surface (TPMS) core structure is proposed via Fused Deposition Modelling (FDM). A bridging layer and a continuous basalt fiber pre-impregnated by stiff thermoset epoxy resin are utilized to address the issue of overhanging printing for the upper face sheet. Two kinds of TPMS are employed as the core, as well as two kinds of honeycomb. Multi-step printed samples using a bonding process and counterpart samples without fiber were prepared for the comparison. 3-point bending tests were conducted and a finite element model which can represent the structure characteristic is proposed to investigate the mechanical properties. The results show that the integrated printed sample exhibits better performance in terms of printing quality, flexural modulus, strength and energy absorption (EA) compared with the multi-step printed sample. It has an excellent ability to avoid the catastrophic damage which is usually encountered in the multi-step printed sample due to the introduction of brittle epoxy resin, showing a notable 162.88 % augmentation in specific energy absorption (SEA). The significant improvement lies in that it uses the reinforcement of fiber and the energy absorption capacity of core to full advantage via the strong binding. In addition, as one kind of TPMS, Schwarz Primary structure exhibits the maximum flexural modulus, strength and energy absorption among the four cores. The proposed design and fabrication methodology pave the way for the creation of high-performance sandwich panels with different core structures.