A semiparametric additive-multiplicative intensity function for recurrent events data under two competing risks have been supposed in this paper. The model contains unknown baseline hazard function that defined separately intensity function for different competing risks effects on subjects failure. The presented model is based on regression parameters for effective covariates and frailty variable which describe correlation between terminal event and recurrent events and personal difference of under study subjects. The model support right censored and informative censored survival data. For estimating unknown parameters, numerical methods have been used and baseline hazard parameters are approximated using Taylor series expansion. A simulation study and application of the model to the bone marrow transplantation data are performed to illustrate the performance of the proposed model.