A new classes of three-step Newton’s methods based on power means Newton’s method has been developed, where two existing numerical methods can be regarded as particular cases of the present method. It is shown that the order of convergence of the proposed methods is six. Also, the efficiency index of the present methods is 1.565, which is better than Newton’s method 1.414. It is observed that our method takes less number of iterations than Newton’s method. Few sixth order methods are compared with the present method where the numbers of iterations for those methods are either same or more than the present methods. Some examples are given to illustrate the performance of the present methods.