Laser-induced graphene (LIG) has the advantages of one-step fabrication, prominent mechanical performance, as well as high conductivity; it acts as the ideal material to fabricate flexible strain sensors. In this study, a wearable flexible strain sensor consisting of three-dimensional (3D) wavy LIG and silicone rubber was reported. With a laser to scan on a polyimide film, 3D wavy LIG could be synthesized on the wavy surface of a mold. The wavy-LIG strain sensor was developed by transferring LIG to silicone rubber substrate and then packaging. For stress concentration, the ultimate strain primarily took place in the troughs of wavy LIG, resulting in higher sensitivity and less damage to LIG during stretching. As a result, the wavy-LIG strain sensor achieved high sensitivity (gauge factor was 37.8 in a range from 0% to 31.8%, better than the planar-LIG sensor), low hysteresis (1.39%) and wide working range (from 0% to 47.7%). The wavy-LIG strain sensor had a stable and rapid dynamic response; its reversibility and repeatability were demonstrated. After 5000 cycles, the signal peak varied by only 2.32%, demonstrating the long-term durability. Besides, its applications in detecting facial skin expansion, muscle movement, and joint movement, were discussed. It is considered a simple, efficient, and low-cost method to fabricate a flexible strain sensor with high sensitivity and structural robustness. Furthermore, the wavy-LIG strain senor can be developed into wearable sensing devices for virtual/augmented reality or electronic skin.