Cross-Platform Social Relationship Prediction (CPSRP) aims to utilize users' data information on multiple platforms to enhance the performance of social relationship prediction, thereby promoting socioeconomic development. Due to the highly sensitive nature of users' data in terms of privacy, CPSRP typically introduces various privacy-preserving mechanisms to safeguard users' confidential information. Although the introduction mechanism guarantees the security of the users' private information, it tends to degrade the performance of the social relationship prediction. Additionally, existing social relationship prediction schemes overlook the interdependencies among items invoked in a user behavior sequence. For this purpose, we propose a novel privacy-preserve Federated Social Relationship Prediction with Contrastive Learning framework called FSRPCL, which is a multi-task learning framework based on vertical federated learning. Specifically, the users' rating information is perturbed with a bounded differential privacy technology, and then the users' sequential representation information acquired through Transformer is applied for social relationship prediction and contrastive learning. Furthermore, each client uploads their respective weight information to the server, and the server aggregates the weight information and distributes it purposes to each client for updating.Numerous experiments on real-world datasets prove that FSRPCL delivers exceptional performance in social relationship prediction and privacy preservation, and effectively minimizes the impact of privacy-preserving technology on social relationship prediction accuracy.