Agent-based models (ABMs) stand as an essential paradigm for proposing and validating hypothetical solutions or policies aimed at addressing challenges posed by complex systems and achieving various objectives. This process demands labor-intensive endeavors and multidisciplinary expertise. Large language models (LLMs) encapsulating cross-domain knowledge and programming proficiency could potentially alleviate the difficulty of this process. However, LLMs excel in handling sequential information, making it challenging for analyzing the intricate interactions and nonlinear dynamics inherent in ABMs. Additionally, due to the lack of self-evaluation capability of LLMs, relying solely on LLMs is insufficient to effectively accomplish this process. In this paper, we present SAGE, a general solution-oriented ABM generation framework designed for automatic modeling and generating solutions for targeted problems. Unlike approaches reliant on expert handcrafting or resource-intensive neural network training, SAGE establishes a verifier-assisted iterative in-context learning process employing large language models (LLMs) to leverages their inherent cross-domain knowledge for tackling intricate demands from diverse domain scenarios. In SAGE, we introduce an semi-structured conceptual representation expliciting the intricate structures of ABMs and an objective representation to guide LLMs in modeling scenarios and proposing hypothetical solutions through in-context learning. To ensure the model executability and solution feasibility, SAGE devises a two-level verifier with chain-of-thought prompting tailored to the complex interactions and non-linear dynamics of ABMs, driving the iterative generation optimization. Moreover, we construct an evaluation dataset of solution-oriented ABMs from open sources.It contains practical models across various domains.