This paper proposes a Web Software Reliability Growth Model(SRGM) with BurrX Testing Effort Function(TEF) based on Non-homogeneous Poisson Process(NHPP) and develops its application to Web software reliability analysis. The incorporated TEF depicts the relationship between Web workload and calendar time, and solves the problem about high uneven of Web workload. By using the workload data and failure data from Web logs. Experimental results show that the proposed model can be used to describe the actual failure process more faithfully than G-O model, which is often used to analyze Web software.