In this paper, we address some issues in existing seismic hazard closed-form equations and present a novel seismic hazard equation form to overcome these issues. The presented equation form is based on higher-order polynomials, which can well describe the seismic hazard information with relatively high non-linearity. The accuracy of the proposed form is illustrated not only in the seismic hazard data itself but also in estimating the annual probability of failure (APF) of the structural systems. For this purpose, the information on seismic hazard is used in representative areas of the United States (West : Los Angeles, Central : Memphis and Kansas, East : Charleston). Examples regarding the APF estimation are the analyses of existing platform structure and nuclear power plant problems. As a result of the numerical example analyses, it is confirmed that the higher-order-polynomial-based hazard form presented in this paper could predict the APF values of the two example structure systems as well as the given seismic hazard data relatively accurately compared with the existing closed-form hazard equations. Therefore, in the future, it is expected that we can derive a new improved APF function by combining the proposed hazard formula with the existing fragility equation.