Some interesting recent studies have shown that safe feature elimination screening algorithms are useful alternatives in solving large scale and/or ultra-high-dimensional Lasso-type problems. However, to the best of our knowledge, the plausibility of adapting the safe feature elimination screening algorithm to survival models is rarely explored. In this study, we first derive the safe feature elimination screening rule for adaptive Lasso Cox model. Then, using both simulated and real-world datasets, we demonstrate that the resulting algorithm can outperform Lasso Cox and adaptive Lasso Cox prediction methods in terms of its predictive performance. In addition to its good predictive performance, we illustrate that the proposed algorithm has a key computational advantage over the above competing methods in terms of computation efficiency.