Although Chain-of-Thought (CoT) has achieved remarkable success in enhancing the reasoning ability of large language models (LLMs), the mechanism of CoT remains a ``black box''. Even if the correct answers can frequently be obtained, existing CoTs struggle to make the reasoning understandable to human. In this paper, we unveil and causalize CoT from a causal perspective to ensure both correctness and understandability of all reasoning steps (to the best of our knowledge, the first such). We model causality of CoT via structural causal models (SCM) to unveil the reasoning mechanism of CoT. To measure the causality of CoT, we define the CoT Average Causal Effect (CACE) to test the causal relations between steps. For those steps without causality (wrong or unintelligible steps), we design a role-playing causal query algorithm to causalize these steps, resulting a causalized CoT with all steps correct and understandable. Experimental results on both open-source and closed-source LLMs demonstrate that the causal errors commonly in steps are effectively corrected and the reasoning ability of LLMs is significantly improved.