Due to the serious consequence caused by insurers' insolvency, how to accurately predict insolvency becomes a very important issue in this area. Many methods have been developed to do this task by using some firm-level financial information. In this paper, we propose a new approach which incorporates several macroeconomic factors in the model and applies feature selection to eliminate the bad effect of some unrelated variables. In this way, we can obtain a more comprehensive and accurate model. More importantly, our method is based on the state-of-the-art non-kernel fuzzy quadratic surface support vector machine (FQSSVM) model which not only performs superiorly in prediction, but also becomes very applicable to the users. Finally, we conduct some numerical experiments based on the real data of non-lifer insurers from USA to show the predictive power and efficiency of our proposed method compared with other benchmark methods. Specifically, in a reasonable computational time, FQSSVM has the most accurate prediction rate and least Type Ⅰ and Type Ⅱ errors.