In this paper, we investigate channel estimation for a large intelligent surface (LIS) aided multiple-input multiple-output (MIMO) communication system. Due to the close proximity of communication devices and LIS terminal, the desired channels can be modeled as line-of-sight channels which are ill-conditioned. To estimate these channel matrices with high quality, we propose a two-stage channel estimation method. In particular, we employ the conventional time-division duplexing based MIMO channel estimation technique in the first stage to estimate the direct MIMO channel between the end terminals. In the second stage, we propose to use a recently developed bilinear adaptive vector approximate message passing (BAdVAMP) algorithm to estimate ill-conditioned LIS channels. The BAdVAMP method has been shown to be accurate and robust for ill-conditioned dictionary learning problems in compressed sensing. We also propose a phase shift design for the LIS using the estimated channels. Specifically, we formulate an optimization problem that maximizes the total channel gain at the user. A closed-form expression to obtain the phase shift of each passive element in the LIS is also derived. Numerical results show that the proposed BAdVAMP based LIS channel estimation performs better than its counterpart scheme bilinear generalized AMP (BiGAMP), especially when channel matrices are ill-conditioned.