Title: Improving Differentially-Private Deep Learning with Gradients Index Pruning. Abstract: Differential Privacy (DP) provides a formal privacy guarantee preventing adversaries from inferring an individual record from populations. Differentially Private Stochastic Gradient Descent (DPSGD), the widely used method to train a model satisfying DP, inserts randomized noise to the gradients in each iteration but leads to significant accuracy decline, particularly on large and deep models. Facing the curse of dimensionality in differentially-private deep learning, we propose a Gradient Index Pruning (GIP) mechanism, which prunes gradients by a novel index perturbation scheme, to preserve important components of the gradients while reducing their sizes. Our mechanism does not alter the model, but merely adds a noisy top-$k$ pruning step before the conventional gradients noise insertion in DPSGD. It is proven that GIP meets DP, yet improves accuracy over DPSGD. We also present theoretical analysis to show GIP indeed introduces less perturbation to the training. Experiments on a variety of models and datasets have demonstrated that GIP exceeds the state-of-the-art differentially-private deep learning methods by a $1-3\%$ accuracy boost.