Recently, deep learning has demonstrated great success in computer vision with the capability to learn powerful image features from a large training set. However, most of the published work has been confined to solving 2D problems, with a few limited exceptions that treated the 3D space as a composition of 2D orthogonal planes. The challenge of 3D deep learning is due to a much larger input vector, compared to 2D, which dramatically increases the computation time and the chance of over-fitting, especially when combined with limited training samples (hundreds to thousands), typical for medical imaging applications. To address this challenge, we propose an efficient and robust deep learning algorithm capable of full 3D detection in volumetric data. A two-step approach is exploited for efficient detection. A shallow network (with one hidden layer) is used for the initial testing of all voxels to obtain a small number of promising candidates, followed by more accurate classification with a deep network. In addition, we propose two approaches, i.e., separable filter decomposition and network sparsification, to speed up the evaluation of a network. To mitigate the over-fitting issue, thereby increasing detection robustness, we extract small 3D patches from a multi-resolution image pyramid. The deeply learned image features are further combined with Haar wavelet-like features to increase the detection accuracy. The proposed method has been quantitatively evaluated for carotid artery bifurcation detection on a head-neck CT dataset from 455 patients. Compared to the state of the art, the mean error is reduced by more than half, from 5.97 mm to 2.64 mm, with a detection speed of less than 1 s/volume.