Abstarct: In the analysis of survival data, it is usually assumed that any unit will experience the event of interest if it is observed for a sufficiently long time. However, it can be assumed that an unknown proportion of the population under study will never experience the interest event.The Promotion time model, which has a biological motivation, is one of the survival models taking this feature in to account. The survival function of uncured people is estimated by using a Cox proportional hazard model where the logarithm of the baxseline hazard function is specified using Bayesian P-splines. We use a Bayesian frxamework for implementing Statistical inference in the proposed model. The identification issues of the model are discussed and a restricted use of the model when the follow-up of the study is not sufficiently long is suggested. The accuracy of our methodology is assumed through a simulation study and the model is illustrated on a dataset from a Melanoma clinical trial.