In this letter, we propose an efficient federated transfer learning (FTL) framework with client selection for intrusion detection (ID) in mobile edge computing (MEC). Specifically, we leverage federated learning (FL) to preserve privacy by training model locally, and utilize transfer learning (TL) to improve training efficiency by knowledge transfer. For FL, unreliable and low-quality clients should not be selected to participate in the training. Therefore, we integrate FTL with a reinforcement learning (RL)-based client selection scheme to achieve the highest ID accuracy within a budget limit on the number of participating clients. Experimental results show that the FTL significantly improves ID accuracy and communication efficiency as compared with the FL. Furthermore, the FTL framework with RL-based client selection can achieve the highest accuracy within budget, which improves performance while saving cost.