The boundary element method (BEM) has been so far applied to various engineering fields as the discretization method. The BEM, however, has an inherent demerit. The accuracy of the inner-point formula is drastically degraded in the vicinity of the boundary. In order to resolve the above difficulties, the regularization technique has been so far applied to the inner-point formula. In the present paper, the novel approaches are developed for enhancing the accuracy of the inner-point formula in the vicinity of the boundary and their performances are investigated quantitatively by applying it to a three-dimensional problem. In order to obtain the high-accuracy solution in the vicinity of the boundary, two approaches have been proposed in the present study: the high-accuracy regularization and the virtual-region method. The former is a natural extension of the regularization technique, whereas the latter originates from a widely different idea. In the latter, the solution is evaluated through the following procedures: the boundary integral equation is solved on the boundary of the virtual region in which the original region is contained and, subsequently, the solution is evaluated by means of the inner-point formula over the virtual boundary. The results of computations show that the accuracy degradation of the inner-point formula is avoided by means of both the proposed methods. In addition, the accuracies of the proposed methods are higher than that of the regularized inner-point formula. From the above results, we can conclude that the proposed methods, the high-accuracy regularization and the virtual-region method, are suitable for improving the accuracy of the numerical solution of the BEM.