Visual storytelling is a new approach to creative expression based on verbal and figural creativity. The keys to visual storytelling are narrating and drawing over a period of time, which can be beneficial but also demanding on creativity for children. Informed by need-finding investigations, we developed StoryDrawer, a co-creative system that supports visual storytelling for children aged 6–10 years through collaborative drawing between children and artificial intelligence (AI). The system includes a context-based voice agent and two AI-driven collaborative strategies: the real-time transformation of children's telling into drawings, and the generation of abstract sketches with semantic similarity to existing story content. We conducted a 2 × 2 study with 64 children to evaluate the efficacy of StoryDrawer by varying the two strategies in four conditions. The results suggest that StoryDrawer provoked participants' creative and elaborate ideas and contributed to their creative outcomes during an engaging visual storytelling experience.