Accurate stock price prediction is important for investors to reduce investment risks and make informed decisions. Gated Recurrent Unit (GRU) is a deep learning model widely used in stock price prediction due to its superior performance. However, its hyperparameters are usually set based on experience, which is subjective and may lead to poor prediction accuracy and weak generalization ability. In this paper, we propose to optimize the important hyperparameters based on the Nutcracker Optimization Algorithm with Non-linear Conversion Factor (NOA-NCF), to reduce the influence of human factors and enhance prediction accuracy. To substantiate the efficacy of the proposed approach, it has been juxtaposed against other methodologies across six distinct stock index datasets. The experimental outcomes demonstrate that the proposed model achieves superior performance across all datasets, signifying its exceptional capabilities.