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Recently, the vector dirty paper coding (DPC) achievable rate region has been shown to be the capacity region of a multiple-input multiple-output Gaussian broadcast channel (MIMO GBC). With DPC, the multiuser interference noncausally known at the transmitter can be completely removed. In this paper, we present a vector DPC structure for MIMO GBC. It is a generalization of the single antenna superposition dirty paper coding for the scalar Gaussian dirty paper problem proposed by Bennatan et al. In a theoretical random code setting, this construction is shown to be able to achieve the promised rate performance of the MIMO GBC. We also implement it with existing vector quantizer and capacity-achieving channel coding. Combined with iterative decoding, a design example validates the effectiveness of our methods.