Abstract: In this paper we present a multilevel quasi-interpolation scheme based on B-spline basis functions on quartic spline space. This kind of quasi-interpolation is very useful in approximation theory and has sophisticated applications. We further give a convergence analysis and compare the presented method with bivariate quadratic spline. To show capability of the proposed scheme, we apply the method to the numerical integration of two-dimensional singular integrals that defined in the Hadamard finite part sense and then compare the results with 𝐶1 bivariate quadratic spline space. The numerical results reveal that the two-level quasi-interpolation operator outperforms the 𝐶1 bivariate quadratic spline and is very convenient in application.