We present a simple design for a broadband tunable terahertz (THz) metamaterial absorber (MMA) consisting of a complementary cross-oval-shaped graphene (CCOSG) structure and dielectric substrate placed on a continuous metal film. Both numerical simulation and theoretical calculation results indicate that the absorbance is greater than 80% from 1.2 to 1.8 THz, and the corresponding relative bandwidth is up to 40%. Simulated electric field and power loss density distributions reveal that the broadband absorption mainly originates from the excitation of continuous surface plasmon resonance (SPR) on the CCOSG. In addition, the MMA is polarization-insensitive for both transverse-electric (TE) and transverse-magnetic (TM) modes due to the geometry rotational symmetry of the unit-cell structure. Furthermore, the broadband absorption properties of the designed MMA can be effectively tunable by varying the geometric parameters of the unit-cell and chemical potential of graphene. Our results may find promising applications in sensing, detecting, and optoelectronic-related devices.