To solve the problem of incident and controllable characteristics of the multi‐band terahertz absorber, a kind of graphene‐based metamaterial angle‐insensitive and tunable terahertz absorber is proposed. The proposed absorber has single‐band and dual‐band absorption function, and profile parameters are presented by single‐groove and dual‐groove arrays, separately. The results show that the absorber has an absorption peak of 99.30% at 16.0 THz. In addition, the absorption of the absorber can reach 94.56% and 99.11% at 11.4 THz and 26.2 THz. Electromagnetic field energy distribution and the real and imaginary parts of the graphene surface conductivity are analyzed by the finite‐element method as a function of the Fermi level and the terahertz frequency. Moreover, compared with a reported terahertz absorber, the graphene‐based absorber is angle insensitive and tunable by adjusting the Fermi levels of graphene. It is believed that the proposed absorber has great potential in the fields of time‐domain spectroscopy technology and imaging technology.