The potential of automatic task-solving through Large Language Model (LLM)-based multi-agent collaboration has recently garnered widespread attention from both the research community and industry. While utilizing natural language to coordinate multiple agents presents a promising avenue for democratizing agent technology for general users, designing coordination strategies remains challenging with existing coordination frameworks. This difficulty stems from the inherent ambiguity of natural language for specifying the collaboration process and the significant cognitive effort required to extract crucial information (e.g. agent relationship, task dependency, result correspondence) from a vast amount of text-form content during exploration. In this work, we present a visual exploration framework to facilitate the design of coordination strategies in multi-agent collaboration. We first establish a structured representation for LLM-based multi-agent coordination strategy to regularize the ambiguity of natural language. Based on this structure, we devise a three-stage generation method that leverages LLMs to convert a user's general goal into an executable initial coordination strategy. Users can further intervene at any stage of the generation process, utilizing LLMs and a set of interactions to explore alternative strategies. Whenever a satisfactory strategy is identified, users can commence the collaboration and examine the visually enhanced execution result. We develop AgentCoord, a prototype interactive system, and conduct a formal user study to demonstrate the feasibility and effectiveness of our approach.