Video outpainting extends a video beyond its original boundaries by synthesizing missing border content. Compared with image outpainting, it requires not only per-frame spatial plausibility but also long-range temporal coherence, especially when outpainted content becomes visible across time under camera or object motion. We propose GlobalPaint, a diffusion-based framework for spatiotemporal coherent video outpainting. Our approach adopts a hierarchical pipeline that first outpaints key frames and then completes intermediate frames via an interpolation model conditioned on the completed boundaries, reducing error accumulation in sequential processing. At the model level, we augment a pretrained image inpainting backbone with (i) an Enhanced Spatial-Temporal module featuring 3D windowed attention for stronger spatiotemporal interaction, and (ii) global feature guidance that distills OpenCLIP features from observed regions across all frames into compact global tokens using a dedicated extractor. Comprehensive evaluations on benchmark datasets demonstrate improved reconstruction quality and more natural motion compared to prior methods. Our demo page is https://yuemingpan.github.io/GlobalPaint/