A novel coronavirus disease 2019 (COVID-19) was detected and has spread rapidly across various countries around the world since the end of the year 2019. Computed Tomography (CT) images have been used as a crucial alternative to the time-consuming RT-PCR test. However, pure manual segmentation of CT images faces a serious challenge with the increase of suspected cases, resulting in urgent requirements for accurate and automatic segmentation of COVID-19 infections. Unfortunately, since the imaging characteristics of the COVID-19 infection are diverse and similar to the backgrounds, existing medical image segmentation methods cannot achieve satisfactory performance. In this article, we try to establish a new deep convolutional neural network tailored for segmenting the chest CT images with COVID-19 infections. We first maintain a large and new chest CT image dataset consisting of 165,667 annotated chest CT images from 861 patients with confirmed COVID-19. Inspired by the observation that the boundary of the infected lung can be enhanced by adjusting the global intensity, in the proposed deep CNN, we introduce a feature variation block which adaptively adjusts the global properties of the features for segmenting COVID-19 infection. The proposed FV block can enhance the capability of feature representation effectively and adaptively for diverse cases. We fuse features at different scales by proposing Progressive Atrous Spatial Pyramid Pooling to handle the sophisticated infection areas with diverse appearance and shapes. The proposed method achieves state-of-the-art performance. Dice similarity coefficients are 0.987 and 0.726 for lung and COVID-19 segmentation, respectively. We conducted experiments on the data collected in China and Germany and show that the proposed deep CNN can produce impressive performance effectively. The proposed network enhances the segmentation ability of the COVID-19 infection, makes the connection with other techniques and contributes to the development of remedying COVID-19 infection.