Warranty claims forecasting plays an increasingly important role not only for preparing financial plans but also for optimizing warranty policy and improving after-sale services. In the case of new products, an important feature is that the new generation of products often has a close connection with the previous generations of products it replaces. Thus, the warranty claims data of the previous generations of products can be used for extracting reliability information of new products. In this context, we propose a warranty claims forecasting model considering usage rate for new products sold with a two-dimensional warranty. The accelerate failure time model is introduced to investigate the effect of usage rate on product degradation. The non-homogeneous Poisson process is used to model failure counts of repairable products and the constrained maximum likelihood estimation method is used to estimate model parameters. The results of data experiments based on both simulation and real data collected from an automobile manufacturer in China show that the proposed model considering the varying usage rate outperforms the traditional models in forecasting the number of warranty claims.