Federated Learning (FL) is a distributed machine learning approach that safeguards privacy by creating an impartial global model while respecting the privacy of individual client data. However, the conventional FL method can introduce security risks when dealing with diverse client data, potentially compromising privacy and data integrity. To address these challenges, we present a differential privacy (DP) federated deep learning framework in medical image segmentation. In this paper, we extend our similarity weight aggregation (SimAgg) method to DP-SimAgg algorithm, a differentially private similarity-weighted aggregation algorithm for brain tumor segmentation in multi-modal magnetic resonance imaging (MRI). Our DP-SimAgg method not only enhances model segmentation capabilities but also provides an additional layer of privacy preservation. Extensive benchmarking and evaluation of our framework, with computational performance as a key consideration, demonstrate that DP-SimAgg enables accurate and robust brain tumor segmentation while minimizing communication costs during model training. This advancement is crucial for preserving the privacy of medical image data and safeguarding sensitive information. In conclusion, adding a differential privacy layer in the global weight aggregation phase of the federated brain tumor segmentation provides a promising solution to privacy concerns without compromising segmentation model efficacy. By leveraging DP, we ensure the protection of client data against adversarial attacks and malicious participants.