A oilfield after exploration and development for nearly 40 years, the development potential of existing target layers has been limited; therefore, it is urgent to find new layers. The most realistic target layers are the layers in the basement buried hill. However, the complex distribution of fractures limits the exploration and development in this area. Based on the detailed interpretation of the structures of the top bedrock, this paper uses the post-stack seismic data by the quantitative fracture prediction technique of tensor direction field (SMI) to predict bedrock fractures. The research indicates that (1) there are two fracture development stages in the bedrock of the A oilfield, including the early and late stages. The early fractures surrounded the bedrock-buried hills, which reworked the bedrock reservoirs and controlled the development of pores. The late fractures were mainly distributed in the NE direction, which further communicated with the bedrock reservoirs and improved the reservoir permeability. (2) The coupling of fractures in two stages is the key factor for bedrock accumulation. (3) Three favorable fracture zones were developed, covering an area of about 18 km2. The research results have a certain reference for predicting bedrock fractures in other areas.