This paper analytically discusses the characteristics of boundary crisis in a mo del of impact oscillator,and proves that the scaling behavior of the life time after crisis follows the rule τ-ε-γ and γ=ln|β2|ln|β1β2|.Here β1 and β2 are the unstab le and stable eigenvalues,respectively,of a saddle node on the basin boundary of a chaotic attractor.This rule is completely different from that in everywhere-s mooth maps.