In this paper, we propose a new acquisition function based on local search for active super-level set estimation. Conventional acquisition functions for level set estimation problems are considered to struggle with problems where the threshold is high, and many points in the upper-level set have function values close to the threshold. The proposed method addresses this issue by effectively switching between two acquisition functions: one rapidly finds local level set and the other performs global exploration. The effectiveness of the proposed method is evaluated through experiments with synthetic and real-world datasets.