Handwritten Text Line Segmentation (HTLS) is a low-level but important task for many higher-level document processing tasks like handwritten text recognition. It is often formulated in terms of semantic segmentation or object detection in deep learning. However, both formulations have serious shortcomings. The former requires heavy postprocessing of splitting/merging adjacent segments, while the latter may fail on dense or curved texts. In this paper, we propose a novel Line Counting formulation for HTLS – that involves counting the number of text lines from the top at every pixel location. This formulation helps learn an end-to-end HTLS solution that directly predicts per-pixel line number for a given document image. Furthermore, we propose a deep neural network (DNN) model LineCounter to perform HTLS through the Line Counting formulation. Our extensive experiments on the three public datasets (ICDAR2013-HSC [1], HIT-MW [2], and VML-AHTE [3]) demonstrate that LineCounter outperforms state-of-the-art HTLS approaches. Source code is available at https://github.com/Leedeng/LineCounter.