The purpose of this paper is to give a sufficient condition for convergence of a multisummable power series. Previously, similar results had been obtained for formal solutions of ordinary differential equations and also of a completely integrable Pfaffian system. In those cases, proof was based heavily on the form of equations. But, in relatively recent developement, it was shown that formal solutions of ordinary differential equations at an irregular singular point are generally multisummable. In this paper, proof of convergence is totally independent of any equations and based only on multisummability of power series.