The ability to automatically complete a partial sketch that depicts a complex scene, e.g., "a woman chatting with a man in the park", is very useful. However, existing sketch generation methods create sketches from scratch; they do not complete a partial sketch in the style of the original. To address this challenge, we introduce AutoSketch, a styleaware vector sketch completion method that accommodates diverse sketch styles. Our key observation is that the style descriptions of a sketch in natural language preserve the style during automatic sketch completion. Thus, we use a pretrained vision-language model (VLM) to describe the styles of the partial sketches in natural language and replicate these styles using newly generated strokes. We initially optimize the strokes to match an input prompt augmented by style descriptions extracted from the VLM. Such descriptions allow the method to establish a diffusion prior in close alignment with that of the partial sketch. Next, we utilize the VLM to generate an executable style adjustment code that adjusts the strokes to conform to the desired style. We compare our method with existing methods across various sketch styles and prompts, performed extensive ablation studies and qualitative and quantitative evaluations, and demonstrate that AutoSketch can support various sketch scenarios.