Automated breast ultrasound (ABUS) is a new and promising tool for diagnosing breast cancer. However, reviewing ABUS images is extremely time-consuming and oversight errors could happen. We propose a novel 3D convolutional network for automatic cancer detection in ABUS. Our contribution is twofold. First, we propose a threshold loss function to provide voxel-level adaptive threshold for discriminating cancer and non-cancer, thus achieving high sensitivity with low FPs. Second, we propose a densely deep supervision (DDS) mechanism to improve the sensitivity significantly by utilizing multi-scale discriminative features of all layers. Both class-balanced cross entropy loss and overlap loss are employed to enhance DDS performance. The efficacy of the proposed network is validated on a dataset of 196 patients with 661 cancer regions. The 4-fold cross-validation experiments show our network obtains a sensitivity of 93% with 2.2 FPs per ABUS volume. Our proposed novel network can provide an accurate and automatic cancer detection tool for breast cancer screening by maintaining high sensitivity with low FPs.