We study a continuous analogue of Newton method for solving the nonlinear equation $$ varphi (z) =0, $$ where $varphi(z)$ holomorphic function and $0inoverline{varphi ( D)}$. It is proved that this method converges, to the solution for each initial data $zin D$, if and only if $varphi(z)$ is a star-like function with respect to either an interior or a boundary point. Our study is based on the theory of one parameter continuous semigroups. It enables us to consider convergence in the case of an interior as well as a boundary location of the solution by the same approach.