Recent works have increasingly focused on learning decentralized policies for agents as a solution to the scalability challenges in Multi-Agent Reinforcement Learning (MARL), where agents typically share the parameters of a policy network to make action decisions. However, this parameter sharing can impede efficient exploration, as it may lead to similar behaviors among agents. Different from previous mutual information-based methods that promote multi-agent diversity, we introduce a novel multi-agent exploration method called Trajectory Entropy Exploration (TEE). Our method employs a particle-based entropy estimator to maximize the entropy of different agents' trajectories in a contrastive trajectory representation space, resulting in diverse trajectories and efficient exploration. This entropy estimator avoids challenging density modeling and scales effectively in high-dimensional multi-agent settings. We integrate our method with MARL algorithms by deploying an intrinsic reward for each agent to encourage entropy maximization. To validate the effectiveness of our method, we test our method in challenging multi-agent tasks from several MARL benchmarks. The results demonstrate that our method consistently outperforms existing state-of-the-art methods.