This paper proposes the method to accurately predict the 180°basic domain width (Dw) in demagnetized states of the grooved Fe3%Si(110) single crystal with the tilt angle of  out of the sheet surface (β). The evaluation of Dw enables the estimation of the anomalous eddy current losses. In this paper, Dw is optimized to minimize the magnetic Gibbs free energy represented by vector potentials using the finite element method and the conjugate gradient method. The μ*-method is adopted to approximate the magnetization relaxation. The stray field energy generated by the magnetic charges occurring on both grooves cross section and sheet surfaces is considered in our proposed method. The validity of the proposed method was confirmed by comparison with the observed Dw. As a result, we could reveal the β dependence of Dw against the groove depth. Moreover, the theoretical threshold of the domain refinement due to the grooves has been suggested.