One-shot object detection (OSOD) aims to detect all object instances towards the given category specified by a query image. Most existing studies in OSOD endeavor to explore effective cross-image correlation and alleviate the semantic feature misalignment, however, ignoring the phenomenon of the model bias towards the base classes and the generalization degradation on the novel classes. Observing this, we propose a novel framework, namely Base-class Suppression and Prior Guidance (BSPG) network to overcome the problem. Specifically, the objects of base categories can be explicitly detected by a base-class predictor and adaptively eliminated by our base-class suppression module. Moreover, a prior guidance module is designed to calculate the correlation of high-level features in a non-parametric manner, producing a class-agnostic prior map to provide the target features with rich semantic cues and guide the subsequent detection process. Equipped with the proposed two modules, we endow the model with a strong discriminative ability to distinguish the target objects from distractors belonging to the base classes. Extensive experiments show that our method outperforms the previous techniques by a large margin and achieves new state-of-the-art performance under various evaluation settings.