Abstract: In order to improve computing efficiency, this paper presents a Kriging surrogate model based numerical method to solve the direct fractional viscoelastic problem. The Kriging surrogate model is set up by making use of the displacement solutions given by FEM and FDM at sample points, and sample points are selected via a Latin Hypercube sampling technique. The computing accuracy and efficiency of the proposed method are tested via homogeneous/ regionally inhomogeneous fractional viscoelastic numerical examples. The test indicates that the Kriging surrogate model is able to provide a reasonable computing accuracy, and is expected to save considerable amount of computing expense for large scale direct fractional viscoelastic problem which are required to solve repeatedly.