Transformer-based speech recognition (ASR) model with deep layers exhibited significant performance improvement. However, the model is inefficient for deployment on resource constrained devices. Layer pruning (LP) is a commonly used compression method to remove redundant layers. Previous studies on LP usually identify the redundant layers according to a task-specific evaluation metric. They are time-consuming for models with a large number of layers, even in a greedy search manner. To address this problem, we propose CoM-FLP, a fast search LP algorithm based on correlation measure. The correlation between layers is computed to generate a correlation matrix, which identifies the redundancy among layers. The search process is carried out in two steps: (1) coarse search: to determine top K candidates by pruning the most redundant layers based on the correlation matrix; (2) fine search: to select the best pruning proposal among K candidates using a task-specific evaluation metric. Experiments on an ASR task show that the pruning proposal determined by CoMFLP outperforms existing LP methods while only requiring constant time complexity. The code is publicly available at https://github.com/louislau1129/CoMFLP.