Combining deep learning with symbolic logic reasoning aims to capitalize on the success of both fields and is drawing increasing attention. Inspired by DeepLogic, an end-to-end model trained to perform inference on logic programs, we introduce IMA-GloVe-GA, an iterative neural inference network for multi-step reasoning expressed in natural language. In our model, reasoning is performed using an iterative memory neural network based on RNN with a gate attention mechanism. We evaluate IMA-GloVe-GA on three datasets: PARARULES, CONCEPTRULES V1 and CONCEPTRULES V2. Experimental results show DeepLogic with gate attention can achieve higher test accuracy than DeepLogic and other RNN baseline models. Our model achieves better out-of-distribution generalisation than RoBERTa-Large when the rules have been shuffled. Furthermore, to address the issue of unbalanced distribution of reasoning depths in the current multi-step reasoning datasets, we develop PARARULE-Plus, a large dataset with more examples that require deeper reasoning steps. Experimental results show that the addition of PARARULE-Plus can increase the model's performance on examples requiring deeper reasoning depths. The source code and data are available at https://github.com/Strong-AI-Lab/Multi-Step-Deductive-Reasoning-Over-Natural-Language.