The Internet of Things (IoT) will be a main data generation infrastructure for achieving better system intelligence. This paper considers the design and implementation of a practical privacy-preserving collaborative learning scheme, in which a curious learning coordinator trains a better machine learning model based on the data samples contributed by a number of IoT objects, while the confidentiality of the raw forms of the training data is protected against the coordinator. Existing distributed machine learning and data encryption approaches incur significant computation and communication overhead, rendering them ill-suited for resource-constrained IoT objects. We study an approach that applies independent Gaussian random projection at each IoT object to obfuscate data and trains a deep neural network at the coordinator based on the projected data from the IoT objects. This approach introduces light computation overhead to the IoT objects and moves most workload to the coordinator that can have sufficient computing resources. Although the independent projections performed by the IoT objects address the potential collusion between the curious coordinator and some compromised IoT objects, they significantly increase the complexity of the projected data. In this paper, we leverage the superior learning capability of deep learning in capturing sophisticated patterns to maintain good learning performance. Extensive comparative evaluation shows that this approach outperforms other lightweight approaches that apply additive noisification for differential privacy and/or support vector machines for learning in the applications with light data pattern complexities.