Multi-task intersection navigation including the unprotected turning left, turning right, and going straight in dense traffic is still a challenging task for autonomous driving. For the human driver, the negotiation skill with other interactive vehicles is the key to guarantee safety and efficiency. However, it is hard to balance the safety and efficiency of the autonomous vehicle for multi-task intersection navigation. In this paper, we formulate a multi-task safe reinforcement learning with social attention to improve the safety and efficiency when interacting with other traffic participants. Specifically, the social attention module is used to focus on the states of negotiation vehicles. In addition, a safety layer is added to the multi-task reinforcement learning framework to guarantee safe negotiation. We compare the experiments in the simulator SUMO with abundant traffic flows and CARLA with high-fidelity vehicle models, which both show that the proposed algorithm can improve safety with consistent traffic efficiency for multi-task intersection navigation.