Publicly available vessel trajectory data is emitted continuously from the global AIS system. Continuous trajectory similarity search on this data has applications in, e.g., maritime navigation and safety. Existing proposals typically assume an offline setting and focus on finding similarities between complete trajectories. Such proposals are less effective when applied to online scenarios, where similarity comparisons must be performed continuously as new trajectory data arrives and trajectories evolve. We therefore propose a real-time continuous trajectory similarity search method for vessels (ACTIVE). We introduce a novel similarity measure, object-trajectory real-time distance, that emphasizes the anticipated future movement trends of vessels, enabling more predictive and forward-looking comparisons. Next, we propose an efficient continuous similar trajectory search (CSTS) algorithm together with a segment-based vessel trajectory index and a variety of search space pruning strategies that reduce unnecessary computations during the continuous similarity search, thereby further improving efficiency. Extensive experiments on two large real-world AIS datasets offer evidence that ACTIVE is capable of outperforming state-of-the-art methods considerably. ACTIVE significantly reduces index construction costs and index size while achieving a 70% reduction in terms of query time and a 60% increase in terms of hit rate.