We present a hybrid method for spectral reflectivity recovery, using 3D extrapolation as a supplemental method for 3D interpolation. The proposed 3D extrapolation is an extended version of 3D interpolation based on the barycentric algorithm. It is faster and more accurate than the conventional spectral-recovery techniques of principal-component analysis and nonnegative matrix transformation. Four different extrapolation techniques (based on nearest neighbors, circumcenters, in-centers, and centroids) are formulated and applied to recover spectral reflectivity. Under the standard conditions of a D65 illuminant and 1964 $10^{circ}$ observer, all reflectivity data from 1269 Munsell color chips are successfully reconstructed. The superiority of the proposed method is demonstrated using statistical data to compare coefficients of correlation and determination. The proposed hybrid method can be applied for fast and accurate spectral reflectivity recovery in image processing.