It is well-known that Deep Neural Networks can be fooled by adding invisible noise called adversarial examples. Recent work on stochastic neural networks (SNN) shows resistance against adversarial attacks, but these methods are still vulnerable to logits-based attacks. In this paper, we propose a simple but efficient defense method called Robust Logit Stochastic Neural Networks (RL-SNN) that adds a robust block (RL) to a pre-trained SNN model at the inference stage without any additional training cost. The RL block scales and normalizes the logits to prevent attacks to employ large logits. Experiments with different methods show that the proposed RL block can be applied directly to any pre-trained SNN. Tests on two public datasets demonstrate that RL-SNN outperforms previous SNNs methods by a large margin under different attacks. RL-SNN becomes the state-of-the-art under most of attacks evaluated.