Log parsing is a critical step for automated log analysis in complex systems. Traditional heuristic-based methods offer high efficiency but are limited in accuracy due to overlooking semantic context. In contrast, recent LLM-based parsers improve accuracy via semantic understanding but incur high latency from frequent model calls. To address this, we propose SCOPE, the first self-correcting online log parsing method that integrates the strengths of both heuristic and LLM-based paradigms. SCOPE introduces a novel bi-directional tree structure that enables efficient template matching from both forward and reversed directions, resulting in a higher overall matching rate. Additionally, it adopts a two-stage syntactic-semantic collaboration framework: a lightweight NLP model first utilizes POS information for syntax-based matching, while the LLM is selectively invoked as a fallback to handle semantically complex cases when uncertainty remains. This design significantly reduces LLM API usage while maintaining high accuracy, achieving a balance between efficiency and effectiveness. Extensive evaluations on diverse benchmark datasets show that SCOPE outperforms state-of-the-art methods in both accuracy and efficiency. The implementation and datasets are publicly released to facilitate further research.