The flexible strain sensors have drawn widespread consideration because of their features with excellent stretchability, durability and sensitivity. In this work, graphene foam (GF) with three-dimensional (3D) network structure was synthesized by employing the polyurethane (PU) sponges as template, and strain sensors based on the natural rubber (NR)/GF composites were fabricated through a dip-coating method. The effects of pore sizes of GF on the strain sensing performance of sensors were systematically investigated. It was founded that the network structure of GF regulated by the sizes of PU sponges had great influence on the strain sensing performance of sensors. The gauge factors of the sensitivity of NR/GF composites decrease from 1350 to 614 with the increase of the pore sizes of GF in the low strain region. Compared with others, sensor based on NR/GF-15 ppi (mesh number, the number of holes per inch) have the most advantages of high strain sensing sensitivity, intense electrical conductivity and superb signal stability. It can be used to monitor body motion behavior such as finger bending, pronunciation of different words and throat micro-motion.