The surtvep package is an open-source software designed for estimating time-varying effects in survival analysis using the Cox non-proportional hazards model in R. With the rapid increase in large-scale time-to-event data from national disease registries, detecting and accounting for time-varying effects in medical studies have become crucial. Current software solutions often face computational issues such as memory limitations when handling large datasets. Furthermore, modeling time-varying effects for time-to-event data can be challenging due to small at-risk sets and numerical instability near the end of the follow-up period. surtvep addresses these challenges by implementing a computationally efficient Kronecker product-based proximal algorithm, supporting both unstratified and stratified models. The package also incorporates P-spline and smoothing spline penalties to improve estimation (Eilers & Marx, 1996). Cross-validation and information criteria are available to determine the optimal tuning parameters. Parallel computation is enabled to further enhance computational efficiency. A variety of operating characteristics are provided, including estimated time-varying effects, confidence intervals, hypothesis testing, and estimated hazard functions and survival probabilities. The surtvep package thus offers a comprehensive and flexible solution to analyzing large-scale time-to-event data with dynamic effect trajectories.