This paper enhances LLM reasoning through an iterative preference learning process inspired by AlphaZero. Monte Carlo Tree Search collects preference data iteratively, using its look-ahead ability to break instance-level rewards into step-level signals, while outcome validation and stepwise self-evaluation keep intermediate steps consistent, and Direct Preference Optimization updates the policy on the resulting step-level preferences. Theoretical analysis shows the importance of on-policy sampled data, and the method lifts Mistral-7B accuracy to 81.8% on GSM8K, 34.7% on MATH, and 76.4% on ARC-C.