The shipping industry is increasingly threatened by global climate change. Reliable trajectory prediction can be used to perceive potential risks and ensure navigation efficiency. However, many existing studies have not fully considered the impact of complex ocean environmental factors and have only focused on local regions, which are difficult to extend to a global scale. To this end, we propose a deep learning vessel trajectory prediction method fusing discretized meteorological data (TripleConvTransformer). First, we clean the automatic identification system data to form a high-quality spatiotemporal trajectory dataset. Then, we fuse the trajectory data with the meteorological data after feature discretization to deeply mine the motion information of ocean-going ships. Finally, we design three modules, the global convolution, local convolution, and trend convolution modules, based on the simplified transformer model to capture multiscale features. We compare TripleConvTransformer with state-of-the-art prediction models. The experimental results show that in the prediction of the trajectory points in the next 90 min, the smallest root mean square error in terms of longitude and latitude and the highest overall prediction accuracy are achieved using TripleConvTransformer. Our method not only fully considers the influence of meteorological factors in the ocean-going process but also effectively extracts the important information hidden in the data, thus achieving accurate trajectory prediction on a global scale.