In this letter, the fast one-dimensional (1-D) algorithms and their sharing design for 1-D inverse integer transforms of H.264/AVC and VC-1 are proposed by using the matrix decompositions with the sparse matrices and the matrix offset computations. The computational complexities of the proposed fast 1-D 4 times 4 and 8 times 8 inverse integer transforms for H.264/AVC are the same as those of the previous fast methods. Then the shift operations of the proposed fast 1-D inverse integer transform for VC-1 are equivalent to those of the previous fast method. For playback environments, the video decoder can support the multiple modes, which include H.264/AVC and VC-1 video standards. The proposed hardware sharing architecture requires lower hardware cost than the individual and separate design for the VLSI realization.