Porous structure with larger specific surface area is more conducive to ion diffusion for the anode materials of metal-ion batteries. In this work, some 3D porous structures with larger and more pores in three directions were designed based on 2D penta-graphene (PG) nanoribbons. By systematically calculations, it was found two of them (h-PG40 and o-PG36) are both thermally and mechanically stable, even at such high temperatures of 1000 K. The alkali metal-ions of Li, Na, and K can be absorbed and diffuse in the pores of h-PG40/o-PG36, and all the porous structures remain metallic regardless of adsorbed ions. Using ab initio molecular dynamics (AIMD) simulation, the diffusion coefficients of Li, Na, and K at different temperatures were calculated. It is found that Li ions can rapidly diffuse in h-PG40 along three directions, but alkali metal-ions of Na and K with larger radii can rapidly diffuse along larger pores in both structures, and have good rate performance. Based on the diffusion coefficients, the obtained diffusion barriers of Li, Na, and K in the h-PG40/o-PG36 structures were 0.19/0.27, 0.26/0.17, 0.41/0.27 eV, which are considerably smaller compared to the minimum diffusion barrier observed in graphite. As the anode of LIB/SIB/PIB, the theoretical specific capacities of h-PG40 and o-PG36 are above 1451.67/781.67/781.67 and 1116.67/868.52/496.30 mAh·g−1, respectively, and the calculated OCV of both structures are smaller than 1.5 V. This reflects their good specific capacity and cycling performance. This theoretical exploration may open a new frontier in searching more practical 3D porous structures as anode materials for alkali metal-ion batteries.