The purpose of this research is to analyze an airline market in which both low cost carriers (LCCs) and full service carriers (FSCs) coexist. LCCs propose cheaper air ticket prices, but the possibility of late arrival is higher than with FSCs. This research investigates the effect of the introduction of an insurance policy that covers the losses from late arrivals. In relation to this insurance, the following two questions are considered. The first is how the demand for LCC changes when the insurance is introduced. The second is how the introduction of this insurance influences the LCC’s investments to lower the possibility of late arrivals. The main results of this research are as follows. First, the introduction of late-arrival insurance increases the demand for LCC. Second, the impact of the introduction of this insurance becomes high when the possibility of late arrival is high and the insurance premium rate is low; however, the effect of the air ticket price of LCC is ambiguous. Third, the introduction of this insurance reduces an LCC’s optimal investment to lower the possibility of late arrivals.