Survival analysis studies the statistical properties of the time until an event of interest occurs. It has been commonly used to study the effectiveness of medical treatments or the lifespan of a population. However, survival analysis can potentially leak confidential information of individuals in the dataset. The state-of-the-art techniques apply ad-hoc privacy-preserving mechanisms on publishing results to protect the privacy. These techniques usually publish sanitized and randomized answers which promise to protect the privacy of individuals in the dataset but without providing any formal mechanism on privacy protection. In this paper, we propose private mechanisms for parametric survival analysis with Weibull distribution. We prove that our proposed mechanisms achieve differential privacy, a robust and rigorous definition of privacy-preservation. Our mechanisms exploit the property of local sensitivity to carefully design a utility function which enables us to publish parameters of Weibull distribution with high precision. Our experimental studies show that our mechanisms can publish useful answers and outperform other differentially private techniques on real datasets.