Abstract: The Weibull distribution is widely applied in repeated claim of quantized life-insurance model，but also is the theoretical basis of reliability analysis and life-insurance model；meanwhile，the Weibull distribution is the extension of exponential distribution. This paper used the knowledge of classical probability theory and mathematics risk theory，towards the insurance problem which the individual claim sum obeyed the Weibull distribution，with establishment of reasonable mathematics model，deduced the explicit expression of ultimate ruin probability，and obtained its asymptotic estimation.

Key words: Weibull distribution, ruin probability, asymptotic estimation, explicit expression