Unlike block cipher, stream ciphers are relatively simple and widely use linear operation, so there is often a strong correlation between the power of attack point and other power components, making it difficult to implement power analysis attacks. For the aforementioned situation, a chosen-Initial Vector (IV) correlation power analysis attack on synchronous stream cipher Grain-128 was proposed. First, the attack point and its power consumption model were gotten by analyzing the property of Grain-128's output function h(x). Then the correlation between the power of attack point and other power components was eliminated by choosing specific initial vectors, and the key problem facing the energy attacks was solved. Finally, a verification experiment was conducted based on power analysis tool PrimeTimePX. The results show that the scheme can implement 23 rounds attack and recover 46 bits key with only 736 initial vectors.