Efficient and robust cell detection serves as a critical prerequisite for many subsequent biomedical image analysis methods and computer-aided diagnosis (CAD). It remains a challenging task due to touching cells, inhomogeneous background noise, and large variations in cell sizes and shapes. In addition, the ever-increasing amount of available datasets and the high resolution of whole-slice scanned images pose a further demand for efficient processing algorithms. In this paper, we present a novel structured regression model based on a proposed fully residual convolutional neural network for efficient cell detection. For each testing image, our model learns to produce a dense proximity map that exhibits higher responses at locations near cell centers. Our method only requires a few training images with weak annotations (just one dot indicating the cell centroids). We have extensively evaluated our method using four different datasets, covering different microscopy staining methods (e.g., H & E or Ki-67 staining) or image acquisition techniques (e.g., bright-filed image or phase contrast). Experimental results demonstrate the superiority of our method over existing state of the art methods in terms of both detection accuracy and running time.