Iterative methods, play an important role in computational sciences. In this chapter, we present new semilocal and local convergence results for the Newton-Kantorovich method. These new results extend the applicability of the Newton-Kantorovich method on approximate zeros by improving the convergence domain and ratio given in earlier studies. These advantages are also obtained under the same computational cost. Numerical examples where the old sufficient convergence criteria are not satisfied but the new convergence criteria are satisfied are also presented in this chapter.