In this paper, we propose FCHD-Fully Convolutional Head Detector, an end-to-end trainable head detection model. Our proposed architecture is a single fully convolutional network which is responsible for both bounding box prediction and classification. This makes our model lightweight with low inference time and memory requirements. Along with run-time, our model has better overall average precision (AP) which is achieved by selection of anchor sizes based on the effective receptive field of the network. This can be concluded from our experiments on several head detection datasets with varying head counts. We achieve an AP of 0.70 on a challenging head detection dataset which is comparable to some standard benchmarks. Along with this our model runs at 5 FPS on Nvidia Quadro M1000M for VGA resolution images. Code is available at https://github.com/aditya-vora/FCHD-Fully-Convolutional-Head-Detector.