Wavelet analysis has been the focus of active research for twenty years, both in theory and applications. In this work, we develop the concept of a class of multiple vector-valued trivariate wavelet wraps with a dilation matrix. A new method for constructing multiple vector-valued trivariate wavelet wraps is proposed. Their characters are investigated by means of operator technique, time-frequency analysis method and matrix theory. There orthogonality formulas regarding the wavelet wraps are provided. Orthogonality decomposition relation formulas of the space L2(R3, Cr×r) are obtained by constructing a series of subspaces of the multiple vector-valued wavelet wraps. Furthermore, several orthonormal wavelet wrap bases of space L2(R3, Cr×r) are constructed from the wavelet wraps. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. Relation to theoretical physics is also discussed.