For the time-to-failure data with competing risks, cumulative incidence functions (CIFs) are commonly estimated using nonparametric methods. If the cases of events due to the cause of primary interest are infrequent relative to other cause of failure, nonparametric methods may result in rather imprecise estimates for CIF. In such cases, Bryant et al. (2004) suggested to model the cause-specific hazard of primary interest parametrically, while accounting for the other modes of failure using nonparametric estimator. We represented the semiparametric cumulative incidence estimator and extended to the model of Weibull and log-normal distribution. We also conducted simulations to access the performance of the semiparametric cumulative incidence estimators and to investigate the impact of model misspecification in log-normal cause-specific hazard model.