Temporally localizing actions in a video is a fundamental challenge in video understanding. Most existing approaches have often drawn inspiration from image object detection and extended the advances, e.g., SSD and Faster R-CNN, to produce temporal locations of an action in a 1D sequence. Nevertheless, the results can suffer from robustness problem due to the design of predetermined temporal scales, which overlooks the temporal structure of an action and limits the utility on detecting actions with complex variations. In this paper, we propose to address the problem by introducing Gaussian kernels to dynamically optimize temporal scale of each action proposal. Specifically, we present Gaussian Temporal Awareness Networks (GTAN)a new architecture that novelly integrates the exploitation of temporal structure into an one-stage action localization framework. Technically, GTAN models the temporal structure through learning a set of Gaussian kernels, each for a cell in the feature maps. Each Gaussian kernel corresponds to a particular interval of an action proposal and a mixture of Gaussian kernels could further characterize action proposals with various length. Moreover, the values in each Gaussian curve reflect the contextual contributions to the localization of an action proposal. Extensive experiments are conducted on both THUMOS14 and ActivityNet v1.3 datasets, and superior results are reported when comparing to state-of-the-art approaches. More remarkably, GTAN achieves 1.9% and 1.1% improvements in mAP on testing set of the two datasets.