This study presents a dynamic cube attack on the algorithm Grain-v1 which has resisted all the key-recovery attacks in the single key model. The dynamic cube attack finds the secret key by using distinguishers obtained from structural weaknesses of a cipher. The main idea of the attack lies in simplifying the cipher's output function. After making it simpler, the attack is able to exploit a distinguishing attack to recover the secret key. In this study, the authors first find the appropriate simplifications for Grain-v1. Then, they apply their attack to the algorithm by using a new framework and a new smart choice technique for the classification of initial value bits. Finally, the authors simulate the attack to find the suitable attack parameters having 73% success rate. Their attack runs in a practical time and recovers all the key bits when the number of initialisation rounds in Grain-v1 is reduced to 100 of 160. The attack is faster than exhaustive search by a factor of 238.