The hybrid quantum–classical learning scheme provides a prominent way to achieve quantum advantages on near-term quantum devices. A concrete example toward this goal is the quantum neural network (QNN), which has been developed to accomplish various supervised learning tasks such as classification and regression. However, there are two central issues that remain obscure when QNN is exploited to accomplish classification tasks. First, a quantum classifier that can well balance the computational cost such as the number of measurements and the learning performance is unexplored. Second, it is unclear whether quantum classifiers can be applied to solve certain problems that outperform their classical counterparts. Here we devise a Grover-search based quantum learning scheme (GBLS) to address the above two issues. Notably, most existing QNN-based quantum classifiers can be seamlessly embedded into the proposed scheme. The key insight behind our proposal is reformulating the classification tasks as the search problem. Numerical simulations exhibit that GBLS can achieve comparable performance with other quantum classifiers under various noise settings, while the required number of measurements is dramatically reduced. We further demonstrate a potential quantum advantage of GBLS over classical classifiers in the measure of query complexity. Our work provides guidance to develop advanced quantum classifiers on near-term quantum devices and opens up an avenue to explore potential quantum advantages in various classification tasks.