Current connectionist simulations require huge computational resources. We describe a neural network simulator for the IBM GF11, an experimental SIMD machine with 566 processors and a peak arithmetic performance of 11 Gigaflops. We present our parallel implementation of the backpropagation learning algorithm, techniques for increasing efficiency, performance measurements on the NetTalk text-to-speech benchmark, and a performance model for the simulator. Our simulator currently runs the back-propagation learning algorithm at 900 million connections per second, where each "connection per second" includes both a forward and backward pass. This figure was obtained on the machine when only 356 processors were working; with all 566 processors operational, our simulation will run at over one billion connections per second. We conclude that the GF11 is well-suited to neural network simulation, and we analyze our use of the machine to determine which features are the most important for high performance.