Automated segmentation methods are critical for early detection, prompt actions, and immediate treatments in reducing disability and death risks of brain infarction. This paper aims to develop a fully automated method to segment the infarct lesions from T1-weighted brain scans. As a key novelty, the proposed method combines variational mode decomposition and deep learning-based segmentation to take advantages of both methods and provide better results. There are three main technical contributions in this paper. First, variational mode decomposition is applied as a pre-processing to discriminate the infarct lesions from unwanted non-infarct tissues. Second, overlapped patches strategy is proposed to reduce the workload of the deep-learning-based segmentation task. Finally, a three-dimensional U-Net model is developed to perform patch-wise segmentation of infarct lesions. A total of 239 brain scans from a public dataset are utilized to develop and evaluate the proposed method. Empirical results reveal that the proposed automated segmentation can provide promising performances with an average dice similarity coefficient (DSC) of 0.6684, intersection over union (IoU) of 0.5022, and average symmetric surface distance (ASSD) of 0.3932, respectively.