Abstract: The goal of computer generated holography (CGH) is to synthesize custom illumination patterns by shaping the wavefront of a coherent light beam. Existing algorithms for CGH rely on iterative optimization with a fundamental trade-off between hologram fidelity and computation speed, making them inadequate for high-speed holography applications such as optogenetic photostimulation, optical trapping, or virtual reality displays. We propose a new algorithm, DeepCGH, that relies on a convolutional neural network to eliminate iterative exploration and rapidly synthesize high resolution holograms with fixed computational complexity. DeepCGH is an unsupervised model which can be tailored for specific tasks with customizable training data sets and an explicit cost function. Results show that our method computes 3D holograms at record speeds and with better accuracy than existing techniques.