A bounded form of the hypersingular Helmholtz integral equation for 3-D acoustic problems is developed in this paper. All integrals with singular kernels are regularized within each regular surface element, in the sense of Kellogg, with twice continuous differentiability. The standard Gaussian quadrature formula is applied without any special treatment for all the computational points. The collocation points are chosen to be the Gauss–Legendre nodes and no interpolation function is assumed for acoustic variables.