Ground-penetrating radar (GPR) enables the noninvasive detection of various subsurface objects such as pipes and stones. The location and size of the object in the medium could be obtained by fitting the generated hyperbolic signatures within the GPR B-scan and analyzing its parameters. In this article, GPR-Former is proposed for automatic target detection and hyperbola fitting on GPR B-scan images. We have designed a transformer-based neural network to extract features to directly regress the parameters of hyperbolic signatures in the GPR B-scan data to detect targets beneath the ground automatically. A symmetry-constrained analytical solution for the hyperbolic parameters is proposed to refine the parameters derived from the transformer network, serving the extraction and analysis of buried objects in underground opaque spaces. Experiments are conducted on three datasets for the qualitative and quantitative validation of the GPR-Former, including ground-penetrating radar detection of submarine pipelines and land pipelines. Results show that the proposed method is able to automatically and efficiently extract hyperbolas from GPR B-scan images. True hyperbola-point precision (TP_Pre) and true hyperbola-point recall (TP_Rec) metrics are introduced to evaluate performances in parametric hyperbola extraction and fitting. The results show that the TP_Pre and TP_Rec of the proposed method reach 0.867, 0.402, and 0.744 and 0.762, 0.736, and 0.723, with an improvement of 6%, 22%, and 4% compared with the state-of-the-art methods (C3 algorithm and migration learning-based method proposed by Yang), respectively.