At EUROCRYPT 2009, Dinur and Shamir proposed a new type of algebraic attacks named cube attack. Grain is one of the 3 final hardware-oriented stream ciphers in the eSTREAM portfolio, which takes an 80-bit secret key and a 64-bit initial vector as input and produces its keystream after 160 rounds of initialization. Applying cube attack on Grain with 70 initialization rounds, the study finds that 15-bit secret key can be recovered and can find 4 linear equations on another 23 bits of the secret key. Moreover, 1-bit secret key can be recovered by applying cube attack on Grain with 75 initialization rounds.