Cryo-electron tomography (Cryo-ET) is an electron microscopy technique that plays an important role in structural biology by reconstructing structures of biological macromolecules in their native environment. In cryo-ET images, also called tomograms, macromolecules are detected through particle picking for their structural reconstruction. Automated particle picking is essential for processing large volumes of cryo-ET data. Although deep learning-based object detection models have achieved excellent performance in many applications, their adoption in particle picking for tomograms remains limited due to low signal-to-noise ratios (SNRs) of cryo-ET images, typically below 0.1. So far, studies on particle picking techniques for tomograms have chosen segmentation models for accuracy. Different from these studies, we solve the problem as a 3D object detection task. Specifically, we have developed a one-stage detection model that locates and classifies particles in 3D tomograms with high efficiency and competitive accuracy. Unlike segmentation models, our model requires only location and class information of particles but not their geometry information for training. Experiments show that our model achieves detection accuracy similar as that of state-of-the-art segmentation models on the SHREC2020 dataset of synthetic images. But its detection speed is about ten times faster than the fastest segmentation model. Our model also achieves good performance on the EMPIAR-10045 dataset of real cryo-ET images. Source code and data of this work are openly accessible at: http://github.com/cbmigroup/3DFastParticleDetection.