Twenty percent of French non-fuel poor households will fall into fuel poverty. The existence of energy insurance can reduce this percentage. This article focuses on non-fuel poor households that can buy insurance that provides a basic level of energy for one year after a significant loss of income. A model of household willingness to pay for energy insurance is proposed. Several simulations are performed with French data. Given the values of the utility function parameters and the energy prices, this willingness to pay depends on the probability of loss of income wich dffers according to the income deciles. This willingness is not a monotonously decreasing function of income. As a result, if the insurer does not wish to mutualize the risks, differentiated contracts will be proposed. These prices resulting from the simulations carried out are in line with the energy insurance prices currently proposed. These prices enable such insurance to generate profits for insurers. This inexpensive insurance can help avoid a supply interruption through a minimum service guarantee thereby avoiding significant costs related to fuel poverty.