The typical lightweight cipher LED, proposed in CHES 2011, is applied in the Internet of things (IoT) to provide security for RFID tags and smart cards etc. Fault analysis has become an important method of cryptanalysis to evaluate the security of lightweight ciphers, depending on its fast speed, simple implementation, complex defense, etc. On the basis of the half byte-oriented fault model, we propose new statistical fault analysis on the LED cipher by inducing faults. Simulating experiment shows that our attack can recover its 64-bit and 128-bit secret keys with 99% probability using an SEI distinguisher, a GF distinguisher and a GF-SEI distinguisher, respectively. The attack can be implemented in the ciphertext-only attacking environment to improve the attacking efficiency and decrease the number of faults. It provides vital reference for security analysis of other lightweight ciphers in the Internet of things.