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Hydraulic fracturing is an effective technology used to stimulate hydrocarbon production from unconventional reservoirs. Numerical simulation of the hydraulic fracturing process plays a key role in the design of hydraulic fracturing. However, most of existing models are overly simplified by neglecting the poroelasticity of rock matrix, which may have a substantial effect on the growth of hydraulic fractures, especially in oil and/or water saturated formations. In this study, we developed a fully coupled finite element model for hydraulic fracture propagation in permeable formations by combining XFEM technique with cohesive zone model, and used it to investigate the effects of poroelasticity on the geometry evolution of single fracture which initiated from an injection point. Fluid flow within the fractures, Darcy flow within the rock matrix, hydraulic fractures propagation, and fluid leak-off into the formation are simultaneously taking into account in the model. Then, the model is validated by comparing the results with available analytical solutions. To understand and quantify the poroelastic effects on the propagation of hydraulic fracture, several cases with different matrix permeability, leak-off coefficients, and bulk modulus of pore fluid are performed. The simulation results show that the total volume of leakage is controlled by the combined action of matrix permeability and leak-off coefficient. The fracture aperture and length decrease with the increase of matrix permeability or leak-off coefficient, while as the bulk moduli of pore fluid increases, the fracture aperture and length tend to increase.