A switching device is required to build a realistic network which can handle the explosive growth of network traffic. However, the drawback of the switching device is mainly focused on the blocking problem. Previous studies have presented the solutions in the quantum context to avoid blocking at the expense of increasing packet loss and the exponential size of quantum gates. In this paper, we design a fully non-blocking quantum switch using the linear number O(N2) of quantum SWAP gates. Comparisons with a previously proposed quantum self-routing packet switch is also presented in terms of the hardware complexity, the propagation delay and packet loss probability