Wavelet analysis has many applications in scientific areas such as computer graphics, image processing, numerical algorithms and signal denoising. In general, a wavelet is derived from a refinable function vector via a multiresolution analysis. In this paper, we presented a novel notion of generalized Hermite interpolating refinable function vector. In terms of its mask, several properties (such as interpolation property, symmetry property and approximation property) with respect to generalized Hermite interpolating refinable function vector. We shall present an example at the end of this paper.