This paper proposes a novel approach to low complexity soft input decoding for lattice reduction-aided MIMO receivers. The proposed approach feeds a soft input decoder with soft signals made from hard decision signals generated by using a lattice reduction-aided linear detector. The soft signal is a weighted-sum of some candidate vectors that are near by the hard decision signal coming out from the lattice reduction-aided linear detector. This paper proposes a technique to adjust the weight adapt to the channel for the higher transmission performance. The transmission performance is evaluated in a 4 x 4 MIMO channel. When a serial interference canceller is used as the linear detector, the proposed technique achieves about 2.0 dB better transmission performance at the BER of 10-5 than the decoder fed with the hard decision signals, even though the proposed soft input decoding can be implemented with small additional complexity.