In addition to the policy gradient method, there are other optimization methods such as Q-learning and Monte Calro tree search (MCTS). Most molecular generative models focus on generating molecules from scratch and are not suitable for starting generation from a given arbitrarily molecule. While this is suitable for generating compound libraries used to search for hit compounds, it is not suitable for cases such as lead optimization, where a candidate compound has already been narrowed down and optimization is performed on that compound. Several methods focusing on starting generation from arbitrary molecules have been proposed. Mol-Cycle-GAN is one of the methods that starts generation from a given molecule. The method is trained using sets of molecules before and after optimization based on the Cycle-GAN generation scheme. Optimization is performed via latent variables, but according to experimental results, it is inferior in terms of performance compared with methods using reinforcement learning. MERMAID is the most relevant method for this study, and it starts generation from an arbitrary molecule by editing SMILES with MCTS and LSTM. However, the generated molecules often deviate significantly from the initial molecules as the optimization progresses. In this study, we developed a molecular optimization method based on molecular graphs, starting from an arbitrary molecule to be explored by MCTS. The use of molecular graphs allows for high similarity with the starting compound, while MCTS allows for efficient generation without prior learning of a specific evaluation function. In addition, a graph neural network model trained on the compound dataset is used to enhance the efficiency of the search. The search is conducted per fragment, but the fragments to be added are generated atom by atom. This allows more appropriate fragments to be added to the current molecule, while avoiding the lack of diversity caused by using a fixed fragment vocabulary.