The recent development of tight oil reservoirs has led to an increase in oil production in the past several years due to the progress in horizontal drilling and hydraulic fracturing. However, the expected oil recovery factor from these reservoirs is still very low. CO2-based enhanced oil recovery is a suitable solution to improve the recovery. One challenge of the estimation of the recovery is to properly model complex hydraulic fracture geometries which are often assumed to be planar due to the limitation of local grid refinement approach. More flexible methods like the use of unstructured grids can significantly increase the computational demand. In this study, we introduce an efficient methodology of the embedded discrete fracture model to explicitly model complex fracture geometries. We build a compositional reservoir model to investigate the effects of complex fracture geometries on performance of CO2 Huff-n-Puff and CO2 continuous injection. The results confirm that the appropriate modelling of the fracture geometry plays a critical role in the estimation of the incremental oil recovery. This study also provides new insights into the understanding of the impacts of CO2 molecular diffusion, reservoir permeability, and natural fractures on the performance of CO2-EOR processes in tight oil reservoirs.