A quantum scale-free network is built up by establishing pairwise entanglement state among nodes. The entanglement percolation threshold values change is compared by random attacking on nodes in network by the way of localization entanglement swapping, and making the nodes targeted failure with the same probability. Results show that the threshold values decrease significantly under random attack and increase significantly under targeted failure, which reflects robustness and fragility of the quantum scale-free network. The scale-free quantum network with entanglement distillation is still robust and fragile under random attack and targeted failure, but which is relatively weaker than that without distillation. It indicates that the real network has a better robustness.