Accurate and high-resolution quantitative precipitation estimation (QPE) plays a crucial role in meteorology and hydrology. However, for acquiring a more accurate QPE, how to depict the complex nonlinear relationship between the radar reflectivity and the true rain rates, as well as adaptively explore the spatial dependencies of precipitation, remains extremely challenging. In this letter, we propose to incorporate the merits of graph convolutional regression networks (GCRNs) and address the aforementioned issues simultaneously in the GCRNs framework. Furthermore, in order to tolerate the variabilities of spatial correlation in the practical precipitation, we expand GCRNs with a multiconvolutional mechanism between the center node and its neighbor rain gauges. Thus, the ability to capture more complicated spatial characteristics of precipitation can be enhanced, and the phenomenon of overwhelming by the neighbor nodes can be released. Extensive experiments were implemented on 12 rainfall processes in Hangzhou, China, 2015. The experimental results confirm that our proposal consistently outperforms the state-of-the-art QPE models.