Fracture initiation is a key factor of hydraulic fracturing, as lack of research on fracture initiation position.The perforation geostress mechanical model of low permeability reservoir is built according to the rock mechanics, seepage mechanics, elastic-plastic mechanics, considering solid-fluid coupling and rock material nonlinearity. Adopting the transient analysis, low-permeability reservoir geostress distribution of different stages is obtained using the finite element, such as drilling - cementing - perforation –fracturing. Determine the fracture initiation position and fracture pressure combining with the rock failure criterion. Calculated on well Ao332-32, the error rate of initiation pressure between test and calculation is 3.5 percent. It is proved that the model is reasonable.