Sum power iterative water-filling (SPIWF) algorithm provides sum-rate-optimal transmission scheme for wireless multiple-input multiple-output (MIMO) broadcast channels (BC), whereas it suffers from its high complexity. In this paper, we propose a new transmission scheme based on a novel block zero-forcing dirty paper coding (Block ZF-DPC) strategy and multiuser-diversity-achieving user selection procedure. The Block ZF-DPC can be considered as an extension of existing ZF-DPC into MIMO BCs. Two user selection algorithms having linear increasing complexity with the number of users have been proposed. One aims at maximizing the achievable sum rate directly and the other is based on Gram-Schmidt Orthogonalization (GSO) and Frobenius norm. The proposed scheme is shown to achieve a sum rate close to the sum capacity of MIMO BC and obtain optimal multiplexing and multiuser diversity gain. In addition, we also show that both selection algorithms achieve a significant part of the sum rate of the optimal greedy selection algorithm at low computation expenditure.