Wireless sensor networks (WSNs) consist of a large number of sensor nodes that monitor the environment and a few base stations that collect the sensor readings. Individual sensor nodes are subject to compromised security because they may be deployed in hostile environments and each sensor node communicates wirelessly. An adversary can inject false reports into the networks via compromised nodes. Furthermore, an adversary can create a wormhole by directly linking two compromised nodes or using out-of-band channels. If these two kinds of attacks occur simultaneously in a network, existing methods cannot defend against them adequately. We thus propose a secure routing method for detecting false report injections and wormhole attacks in wireless sensor networks. The proposed method uses ACK messages for detecting wormholes and is based on a statistical en-route filtering (SEF) scheme for detecting false reports. Simulation results show that the proposed method reduces energy consumption by up to 20% and provide greater network security.