Computational homogenization is a well-employed scheme to calculate the ”averaged” property of the multi-scale materials that have both large computational domain while small characteristic scale. Computational homogenization is designed to solve a special boundary condition problem, while such the computation burden is still quite heavy especially considering large amount of samples of representative volume element (RVE) when the uncertainty quantification is conducted. To circumvent this problem, we have proposed to train a neural operator as an accurate and efficient surrogate model such that a map can be built from the multiscale material property field to the solution field of boundary condition problem. Numerical simulation results have indicated that the multiwavelet-based neural operator performs the best among the selected neural operator candidates. Furthermore, the uncertainty quantification is conducted on the computed homogenized material property. This approach paves the way for efficient computational homogenization process and uncertainty quantification without running the time-consuming finite element or finite volume based simulations.