The NTRU cryptosystem is a public key system based on lattice problems. While its theoretical security has been well studied, little effort has been made to analyze its security against implementation attacks including power analysis attacks. In this paper, we show that a typical software implementation of NTRU is vulnerable to the simple power analysis and the correlation power analysis including a second-order power attack. We also present novel countermeasures to prevent these attacks, and perform experiments to estimate the performance overheads of our countermeasures. According to our experimental results, the overheads in required memory and execution time are only 8.17% and 9.56%, respectively, over a Tmote Sky equipped with an MSP430 processor.