Segmentation is a routine and crucial procedure for the treatment of brain tumors. Deep learning based brain tumor segmentation methods have achieved promising performance in recent years. However, to pursue high segmentation accuracy, most of them require too much memory and computation resources. Motivated by a recently proposed partially reversible U-Net architecture that pays more attention to memory footprint, we further present a novel Memory-Efficient Cascade 3D U-Net (MECU-Net) for brain tumor segmentation in this work, which can achieve comparable segmentation accuracy with less memory and computation consumption. More specifically, MECU-Net utilizes fewer down-sampling channels to reduce the utilization of memory and computation resources. To make up the accuracy loss, MECU-Net employs multi-scale feature fusion module to enhance the feature representation capability. Additionally, a light-weight cascade model, which resolves the problem of small target segmentation accuracy caused by model compression to some extent, is further introduced into the segmentation network. Finally, edge loss and weighted dice loss are combined to refine the brain tumor segmentation results. Experiment results on BraTS 2019 validation set illuminate that MECU-Net can achieve average Dice coefficients of 0.902, 0.824 and 0.777 on the whole tumor, tumor core and enhancing tumor, respectively.