Terahertz (THz) absorbers for imaging, sensing, and detection are in high demand. However, such devices suffer from high manufacturing costs and limited absorption bandwidths. In this study, we presented a low-cost broadband tunable THz absorber based on one-step laser-induced graphene (LIG). The laser-machining-parameter-dependent morphology and performance of the absorbers were investigated. Coarse tuning of THz absorption was realized by changing the laser power, while it was fine-tuned by changing the scanning speed. The proposed structure can achieve over 90% absorption from 0.5 THz to 2 THz with optimized parameters. The LIG method can help in the development of various THz apparatuses.