We developed a One-shot Distributed Algorithm for Cox proportional-hazards model to analyze Heterogeneous multi-center time-to-event data (ODACH) circumventing the need for sharing patient-level information across sites. This algorithm implements a surrogate likelihood function to approximate the Cox log-partial likelihood function that is stratified by site using patient-level data from a lead site and aggregated information from other sites, allowing the baseline hazard functions and the distribution of covariates to vary across sites. Simulation studies and application to a real-world opioid use disorder study showed that ODACH provides estimates close to the pooled estimator, which analyzes patient-level data directly from all sites via a stratified Cox model. Compared to the estimator from meta-analysis, the inverse variance-weighted average of the site-specific estimates, ODACH estimator demonstrates less susceptibility to bias, especially when the event is rare. ODACH is thus a valuable privacy-preserving and communication-efficient method for analyzing multi-center time-to-event data.