Automatic generation of custom instructions is the key to the extensible processors. The generation of custom instructions includes two crucial steps: 1) custom instruction enumeration and 2) custom instruction selection. This letter focuses on the custom instruction enumeration step. Enumerating all custom instruction candidates satisfying architectural constraints from an application graph is a computationally difficult problem. Considering the high complexity of the custom instruction enumeration, we propose a simple but efficient parallel search method based on multidepth graph partitioning for enumerating custom instructions. Experimental results show that the proposed method can give near-linear speedup and outperforms the latest parallel methods.