Metamaterials, composed of subwavelength resonators, have extraordinary electromagnetic properties which rely on the sizes and shapes of the resonance structures rather than their compositions. Recently, achieving electromagnetically induced transparency (EIT) in metamaterial system, also called electromagnetically-induced-transparency-like (EIT-like) analogue, has attracted intense attention. Many studies of EIT-like metamaterials have been reported at microwave, terahertz, and optical frequencies numerically and experimentally. However, most of the EIT-like metamaterials can only control the transmission window by changing the structure size of the metamaterial which restricts the practical applications of the EIT-like metamaterial. Therefore, a broadband tunable EIT-like metamaterials based on graphene in terahertz band is presented in this paper, which consists of a cut-wire as the bright resonator and two couples of H-shaped resonators in mirror symmetry as the dark resonators. The transmissivity of the metamaterial structure is simulated by the software CST Microwave Studio. And the simulation results show that the transmission window of this structure is in a frequency range from 1.05 THz to 1.46 THz, which is attributed to the interference between the plasmon resonance of wire resonators and the LC resonance of H-shaped resonators. In addition, increasing the number of dark mode resonators leads to an increase in transmission window bandwidth. Furthermore, a broadband tunable property of transmission amplitude is realized by changing the Fermi level of graphene. When the graphene Fermi level gradually increases from 0 eV to 1.5 eV, the transmission amplitude of the transmission window gradually decreases from 87% to 20%, which realizes the broadband tunability of transmission window. At the same time, the distribution of the electric field at a central frequency of 1.26 THz is simulated to analyse the transmission mechanism. Finally, the EIT metamaterial samples are prepared and the transmission curves of the samples are tested by terahertz time-domain spectroscopy. Such an EIT-like metamaterial not only realizes the broadband EIT property but also realizes the characteristic of the tunable amplitude of the transmission window, which has potential applications in designing the active slow-light devices, terahertz active filtering and terahertz modulator.