[en] Understanding voluntary contribution in threshold public goods games has important practical implications. To improve contributions and provision frequency, free-rider problem and assurance problem should be solved. Insurance could play a significant, but largely unrecognized, role in facilitating a contribution to provision of public goods through providing insurance compensation against the losses. In this paper, we study how insurance compensation mechanism affects individuals’ decision-making under risk environments. We propose a multi-level threshold public goods game model where two kinds of public goods games (local and global) are considered. Particularly, the global public goods game involves a threshold, which is related to the safety of all the players. We theoretically probe the evolution of contributions of different levels and free-riders, and focus on the influence of the insurance on the global contribution. We explore, in both the cases, the scenarios that only global contributors could buy insurance and all the players could. It is found that with greater insurance compensation, especially under high collective risks, players are more likely to contribute globally when only global contributors are insured. On the other hand, global contribution could be promoted if a premium discount is given to global contributors when everyone buys insurance. (paper: interdisciplinary statistical mechanics)