An entailment tree is a structured reasoning path that clearly demonstrates the process of deriving hypotheses through multiple steps of inference from known premises. It enhances the interpretability of QA systems. Existing methods for generating entailment trees typically employ iterative frameworks to ensure reasoning faithfulness. However, they often suffer from the issue of false feasible steps, where selected steps appear feasible but actually lead to incorrect intermediate conclusions. Moreover, the existing iterative frameworks do not consider error-prone search branches, resulting in error propagation. In this work, we propose SPEH: an iterative entailment tree generation framework with Step feasibility Perception and state Error Handling mechanisms. Step Feasibility Perception enables the model to learn how to choose steps that are not false feasible. State Error Handling includes error detection and backtracking, allowing the model to correct errors when entering incorrect search branches. Experimental results demonstrate the effectiveness of our approach in improving the generation of entailment trees.