Successful automated detection of short needles during an intervention is necessary to allow the physician identify and correct any misalignment of the needle and the target at early stages, which reduces needle passes and improves health outcomes. In this paper, we present a novel approach to detect needle voxels in 3D ultrasound volume with high precision using convolutional neural networks. Each voxel is classified from locally-extracted raw data of three orthogonal planes centered on it. We propose a bootstrap re-sampling approach to enhance the training in our highly imbalanced data. The proposed method successfully detects 17G and 22G needles with a single trained network, showing a robust generalized approach. Extensive ex-vivo evaluations on 3D ultrasound datasets of chicken breast show 25% increase in F1-score over the state-of-the-art feature-based method. Furthermore, very short needles inserted for only 5 mm in the volume are detected with tip localization errors of 0.5 mm, indicating that the tip is always visible in the detected plane.