Recent advances in deep-learning-based applications have attracted a growing attention from the IoT community. These highly capable learning models have shown significant improvements in expected accuracy of various sensory inference tasks. One important and yet overlooked direction remains to provide uncertainty estimates in deep learning outputs. Since robustness and reliability of sensory inference results are critical to IoT systems, uncertainty estimates are indispensable for IoT applications. To address this challenge, we develop ApDeepSense, an effective and efficient deep learning uncertainty estimation method for resource-constrained IoT devices. ApDeepSense leverages an implicit Bayesian approximation that links neural networks to deep Gaussian processes, allowing output uncertainty to be quantified. Our approach is shown to significantly reduce the execution time and energy consumption of uncertainty estimation thanks to a novel layer-wise approximation that replaces the traditional computationally intensive sampling-based uncertainty estimation methods. ApDeepSense is designed for neural net-works trained using dropout; one of the most widely used regularization methods in deep learning. No additional training is needed for uncertainty estimation purposes. We evaluate ApDeepSense using four IoT applications on Intel Edison devices. Results show that ApDeepSense can reduce around 88.9% of the execution time and 90.0% of the energy consumption, while producing more accurate uncertainty estimates compared with state-of-the-art methods.