The localization and segmentation of the novel coronavirus disease of 2019 (COVID-19) lesions from computerized tomography (CT) scans are of great significance for developing an efficient computer-aided diagnosis system. Deep learning (DL) has emerged as one of the best choices for developing such a system. However, several challenges limit the efficiency of DL approaches, including data heterogeneity, considerable variety in the shape and size of the lesions, lesion imbalance, and scarce annotation. In this article, a novel multitask regression network for segmenting COVID-19 lesions is proposed to address these challenges. We name the framework MT-nCov-Net. We formulate lesion segmentation as a multitask shape regression problem that enables partaking the poor-, intermediate-, and high-quality features between various tasks. A multiscale feature learning (MFL) module is presented to capture the multiscale semantic information, which helps to efficiently learn small and large lesion features while reducing the semantic gap between different scale representations. In addition, a fine-grained lesion localization (FLL) module is introduced to detect infection lesions using an adaptive dual-attention mechanism. The generated location map and the fused multiscale representations are subsequently passed to the lesion regression (LR) module to segment the infection lesions. MT-nCov-Net enables learning complete lesion properties to accurately segment the COVID-19 lesion by regressing its shape. MT-nCov-Net is experimentally evaluated on two public multisource datasets, and the overall performance validates its superiority over the current cutting-edge approaches and demonstrates its effectiveness in tackling the problems facing the diagnosis of COVID-19.