Abstract: Recurrent event data usually occur in long-term studies which concern recurrence rates of the disease. In studies of medical sciences, patients who have infected with the disease, like cancer, were conventionally regarded as impossible to be cured. However, with the development of medical sciences, recently those patients were found to be possibly recovered from the disease. The recurrence rate of the events, which is of primary interest, may be affected by the cure rate that may exist. Therefore, we proposed semiparametric statistical analysis for recurrent event data with subjects possibly being cured. In our approach, we present a proportional rate model for recurrence rate with the cure rate adjusted through a Logistic regression model, and develop some estimating equations for estimation of the regression parameters, with their large sample properties, including consistency and asymptotic normality established. Numerical studies under different settings were conducted for assessing the proposed methodology and the results suggest that they work well for practical situations. The approach is applied to a bladder cancer dataset which motivated our study.