Existing gradient-based optimization methods update the parameters locally, in a direction that minimizes the loss function. We study a different approach, symmetry teleportation, that allows the parameters to travel a large distance on the loss level set, in order to improve the convergence speed in subsequent steps. Teleportation exploits parameter space symmetries of the optimization problem and transforms parameters while keeping the loss invariant. We derive the loss-invariant group actions for test functions and multi-layer neural networks, and prove a necessary condition of when teleportation improves convergence rate. We also show that our algorithm is closely related to second order methods. Experimentally, we show that teleportation improves the convergence speed of gradient descent and AdaGrad for several optimization problems including test functions, multi-layer regressions, and MNIST classification.