The electromagnetic induction transparency (EIT) is a phenomenon in which the originally opaque medium becomes transparent under certain resonant electromagnetic fields. It has been seen in applications ranging from nonlinear optics, slow light and optical storage. From the viewpoint of single-frequency, researchers have paid much attention to the realization of broadband electromagnetic induction transparency in recent years. In this paper, a broadband electromagnetic induction transparency effect is investigated theoretically by the finite difference time-domain method. A composite structure based on graphene metasurface which consists of graphene strip with air groove, gallium nitride, silica and titanium dioxide is designed in infrared range. A broadband electromagnetically induced transparency effect could be found in the designed composite structure compared with those in several similar structure. The electromagnetically induced transparency window can be tuned gently by the width of air groove and gallium nitride dielectric slabs. The results show that a wideband electromagnetically induced transparency window of 4 terahertz is found in the infrared frequency range. By comparison with the existing research results, a wider band of electromagnetically induced transparency is found in our structure. We study the physical mechanism of broadband electromagnetically induced transparency from the aspects of structural parameters and electromagnetic field distribution. The thickness w1 of gallium nitride, the width wa and depth h of air groove on graphene strip are discussed in this article. The smaller the length wa or depth h, the wider the EIT band is. The peak of high frequency at which the transmission is near to zero is blue-shifted as h increases. However, red-shift is found as width wa increases. It is found that graphene strip exists as a bright mode. coupling action acts as air groove and gallium nitride slabs function as dark mode, resulting in broadband electromagnetic induced transparency. That is to say, the principle of broadband electromagnetically induced transparency is due to a bright mode coupling in two different forms of dark mode, thus widening the transmission band. This work provides a kind of structure and a design way, to gain the broadband of electromagnetically induced transparency effect. Moreover, it is found that changing the refractive index of background medium, the frequency of high frequency band has a red-shift, the greater change of the refractive index can lead to smaller frequency range. It can be seen that the values of group index ng of three frequency peaks exceeding 25 are observed. The results also show that the slow-light effect and the sensing effect in several frequency ranges are obtained in the proposed structure and potential applications in the optical storage and highly sensitive infrared-band sensor, infrared optical switching, etc.