Electromagnetically induced transparency (EIT) based on dielectric metamaterials has attracted attentions in recent years because of its functional manipulation of electromagnetic waves and high refractive index sensitivity, such as high transmission, sharp phase change, and large group delay, etc. In this paper, an active controlled EIT effect based on a graphene-dielectric hybrid metamaterial is proposed in the near infrared region. By changing the Fermi level of the top-covered graphene, a dynamic EIT effect with a high quality factor (Q-factor) is realized, which exhibits a tunable, slow, light performance with a maximum group index of 2500. Another intriguing characteristic of the EIT effect is its high refractive index sensitivity. In the graphene-covered metamaterial, the refractive index sensitivity is simulated as high as 411 nm/RIU and the figure-of-merit (FOM) is up to 159, which outperforms the metastructure without graphene. Therefore, the proposed graphene-covered dielectric metamaterial presents an active EIT effect in the near infrared region, which highlights its great application potential in deep optical switching, tunable slow light devices, and sensitive refractive index sensors, etc.