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A speed estimation method using the acceleration data measured by a wearable device during exercising on a treadmill is described in this paper. The moving speed is estimated by a regression algorithm that implements a deep convolutional neural network (CNN) model. This model is trained on a set of test speeds for walking and running conditions. The mean square error between the inferred speeds and test speeds is minimized during the training to optimize the internal model parameters. The speed inference mean error is shown to be accurate within 7% and 18% of the actual running and walking test speeds, respectively. The deep CNN model parameters, e.g., data sample size, convolution kernel size, and fully connected layer sizes, are optimized for inference accuracy and sized to enable a compact hardware design. The feasibility of designing a wearable device that can infer speed from the acceleration measurement for wearable applications is demonstrated by device simulation.