The Fine-Gray proportional sub-distribution hazards (PSH) model is among the most popular regression model for competing risks time-to-event data. This article develops a fast safe feature elimination method, named PSH-SAFE, for fitting the penalized Fine-Gray PSH model with a Lasso (or adaptive Lasso) penalty. Our PSH-SAFE procedure is straightforward to implement, fast, and scales well to ultrahigh dimensional data. We also show that as a feature screening procedure, PSH-SAFE is safe in a sense that the eliminated features are guaranteed to be inactive features in the original Lasso (or adaptive Lasso) estimator for the penalized PSH model. We evaluate the performance of the PSH-SAFE procedure in terms of computational efficiency, screening efficiency and safety, run-time, and prediction accuracy on multiple simulated datasets and a real bladder cancer data. Our empirical results show that the PSH-SAFE procedure possesses desirable screening efficiency and safety properties and can offer substantially improved computational efficiency as well as similar or better prediction performance in comparison to their baseline competitors.