This 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 when QR decomposition interference suppression combined with interference cancellation is used over independent Rayleigh fading channel. The different rate LDPC codes can be made by puncturing some rows of a given parity check matrix. This allows to implement a single encoder and decoder for different rate LDPC codes. The performance can be improved by assigning stronger LDPC codes in lower layer than upper layer because the poor SNR of first detected data streams makes error propagation. Keeping the same overall code rates, the V-BLAST system with different rate LDPC codes has the better performance (in terms of Bit Error Rate) than with constant rate LDPC code in fast fading channel.