Deep neural networks (DNNs) have successfully learned useful data representations in various tasks, however, assessing the reliability of these representations remains a challenge. Deep Ensemble is widely considered the state-of-the-art method for uncertainty estimation, but it is very expensive to train and test. MC-Dropout is another alternative method, which is less expensive but lacks the diversity of predictions. To get more diverse predictions in less time, we introduce Randomized ReLU Activation (RRA) framework. Under the framework, we propose two strategies, MC-DropReLU and MC-RReLU, to estimate uncertainty. Instead of randomly dropping some neurons of the network as in MC-Dropout, the RRA framework adds randomness to the activation function module, making the outputs diverse. As far as we know, this is the first attempt to add randomness to the activation function module to generate predictive uncertainty. We analyze and compare the output diversity of MC-Dropout and our method from the variance perspective and obtain the relationship between the hyperparameters and output diversity in the two methods. Moreover, our method is simple to implement and does not need to modify the existing model. We experimentally validate the RRA framework on three widely used datasets, CIFAR10, CIFAR100, and TinyImageNet. The experiments demonstrate that our method has competitive performance but is more favorable in training time and memory requirements.