In this paper, a plasmonically induced transparency (PIT)-like phenomenon in a metasurface composed of a periodic graphene ring and ribbon arrays is studied in the terahertz region. We used the Lorentz oscillator model to analyze the metasurface physically and theoretically. This PIT-like effect can be tuned by alternation of the chemical potential and dimension of the nano-graphene ring and ribbon. The resonance frequency of the PIT-like phenomenon is not sensitive to the incident lightwave angle. As an application of the structure, a refractive index sensor is proposed and simulated. Furthermore, we propose a metasurface composed of a double ring and graphene ribbon to realize the PIT-like effect with three dips. Our results express an appropriate approach for the expansion of mid-infrared absorbers and sensors.