In this paper, we propose vertical Bell laboratories layered space-time (V-BLAST) system based on variable rate low density parity check (LDPC) codes to improve performance of receiver. Because of noise enhancement through zero-forcing, MMSE detection scheme is usually used to improve the performance. We consider MMSE-QR decomposition (QRD) which has the approximately same complexity as zero forcing QRD. The performance can be improved by assigning the lower rate LDPC codes in early detected layers since the poor SNR of early detected data streams makes error propagation in upper layer. The different rate LDPC codes can be made by puncturing some rows of a given parity check matrix. Under the same overall code rate, the V-BLAST system with different rate LDPC codes has the better performance than with constant rate LDPC code in fast fading channel.