Industrial control systems (ICSs) are widely used in critical infrastructures, making them popular targets for attacks to cause catastrophic physical damage. As one of the most critical components in ICSs, the programmable logic controller (PLC) controls the actuators directly. A PLC executing a malicious program can cause significant property loss or even casualties. The number of attacks targeted at PLCs has increased noticeably over the last few years, exposing the vulnerability of the PLC and the importance of PLC protection. Unfortunately, PLCs cannot be protected by traditional intrusion detection systems or antivirus software. Thus, an effective method for PLC protection is yet to be designed. Motivated by these conces, we propose a non-invasive power-based anomaly detection scheme for PLCs. The basic idea is to detect malicious software execution in a PLC through analyzing its power consumption, which is measured by inserting a shunt resistor in series with the CPU in a PLC while it is executing instructions. To analyze the power measurements, we extract a discriminative feature set from the power trace, and then train a long short-term memory (LSTM) neural network with the features of normal samples to predict the next time step of a normal sample. Finally, an abnormal sample is identified through comparing the predicted sample and the actual sample. The advantages of our method are that it requires no software modification on the original system and is able to detect unknown attacks effectively. The method is evaluated on a lab testbed, and for a trojan attack whose difference from the normal program is around 0.63%, the detection accuracy reaches 99.83%.