A polarization-insensitive dual-band terahertz absorber using a single-layer periodic triangle graphene metamaterial structure is presented in this paper. Through constructing the periodic triangle graphene structure with three embedded T-shaped graphene strips, two absorption peaks at 1.98 and 3.68 THz with high absorption rates can be obtained and tuned by the variations of geometric parameters or graphene's Fermi energy levels. Furthermore, the proposed dual-band terahertz absorber possesses the properties of polarization insensitivity and incident angle robustness. This study will have a significant potential for the design of graphene-based absorbers with different working frequencies at the terahertz regime.