Accuracy improvement has been one of the most outstanding issues in the recommender systems research community. Recently, multi-criteria recommender systems that use multiple criteria ratings to estimate overall rating have been receiving considerable attention within the recommender systems research domain. This paper proposes a neural network model for improving the prediction accuracy of multi-criteria recommender systems. The neural network was trained using simulated annealing algorithms and integrated with two samples of single-rating recommender systems. The paper presents the experimental results for each of the two single-rating techniques together with their corresponding neural network-based models. To analyze the performance of the approach, we carried out a comparative analysis of the performance of each single rating-based technique and the proposed multi-criteria model. The experimental findings revealed that the proposed models have by far outperformed the existing techniques.