As the web-server based business is rapidly developed and popularized, how to evaluate and improve the reliability of web-servers has been extremely important. Although a large number of software reliability growth models (SRGMs), including those combined with multiple change-points (CPs), have been available, these conventional SRGMs cannot be directly applied to web software reliability analysis because of the complex web operational profile. To characterize the web operational profile precisely, it should be realized that the workload of a web server is normally non-homogeneous and often observed with the pattern of random impulsive shocks. A web software reliability model with random impulsive shocks and its statistical analysis method are developed. In the proposed model, the web server workload is characterized by a geometric Brownian motion process. Based on a real data set from IIS server logs of ICRMS website (www.icrms.cn), the proposed model is demonstrated to be powerful for estimating impulsive shocks and web software reliability.