Breast tumor segmentation from ultrasound images is one of the key steps that help us characterize and localize tumor regions. However, variable tumor morphology, blurred boundaries, and similar intensity distributions bring challenges for radiologists to segment breast tumors manually. During clinical diagnosis, there are higher demands on the segmentation accuracy and efficiency of breast ultrasound images, so there is an urgent need for an automated method to improve the segmentation accuracy as a technical tool to assist diagnosis. Inspired by the U-net and its many variations, this paper proposed an unpretentious nested U-net (NU-net) for accurate and efficient breast tumor segmentation. The key idea is to utilize U-nets with different depths and shared weights to achieve robust characterization of breast tumors. Specifically, we first utilize the deeper U-net (fifteen layers) as the backbone network to extract more sufficient breast tumor features. Then, we developed a multi-output U-net to be taken as the bond between the encoder and the decoder to enhance the network adaptability for breast tumors with different scales. Finally, the short-connection based on multi-step down-sampling is used to enhance the correlation of long-range information of encoded features. Extensive experimental results with fifteen state-of-the-art segmentation methods on three public breast ultrasound datasets demonstrate that our method has a more competitive segmentation performance on breast tumors. Furthermore, the robustness of our approach is further illustrated by the segmentation of renal ultrasound images. The source code is publicly available on https://github.com/CGPxy/NU-net.