Local causal discovery aims to identify and distinguish the direct causes and effects of a target variable from observational data. Due to the inherent incompleteness of local information, popular methods from global causal discovery often face new challenges in local causal discovery tasks, such as 1) erroneous symmetry constraint tests and the resulting cascading errors in constraint-based methods, and 2) confusion within score-based approaches caused by local spurious equivalence classes. To address the above issues, we propose a Hybrid Local Causal Discovery algorithm, called HLCD. Specifically, HLCD initially utilizes a constraint-based approach with the OR rule to obtain a candidate skeleton, which is subsequently refined using a score-based method to eliminate redundant structures. Furthermore, during the local causal orientation phase, HLCD distinguishes between V-structures and equivalence classes by comparing local structure scores between the two, thereby avoiding orientation interference caused by local equivalence class ambiguities. Comprehensive experiments on 14 benchmark Bayesian networks and two real datasets validate that the proposed algorithm outperforms the existing local causal discovery methods.