The interbody fusion cages are critical implants in spinal fusion surgeries, which stabilize the spine and treat pains resulting from degenerative disc disease. The commercial used poly (ether-ether-ketone) (PEEK) cages are non-porous and manufactured by machining, which cause material waste and insufficient bioactivity. Fused filament fabrication (FFF) technology provides opportunities to fabricate fusion cages with specific shape and intricate porous architectures for bone ingrowth and nutrient exchange. Herein, PEEK-based lattice structures are designed and firstly fabricated by FFF based on three minimal surfaces including Schwarz P (P), Diamond (D) and Gyroid (G). The effects of cellular architecture and unit cell on the compressive properties are investigated. The results demonstrate that D and G surfaces possess superior load-carrying and energy absorption capacity. The prototyping defects in PEEK lattices were lesser than those in PEEK/CF samples. Also, it is notable that the compression performance of FFF-printed samples exhibited a strong anisotropy depending on the printing direction. After printing, annealing is an effective post treatment to further improve the crystallinity and compressive strength of PEEK lattice surfaces. Therefore, the novel PEEK porous structures with optimized mechanical performance show great potentials in the applications as fusion cage implants.