In this paper, a novel channel estimation technique for intelligent reflecting surface (IRS)-aided single-user multiple-input multiple-output (SU-MIMO) systems is proposed. Based on dominant single-path channel approximation for IRS-related channels, the proposed technique conducts parameter estimation instead of straightforward full channel estimation. This makes the proposed technique practical with low training overhead, compared to the typical channel estimations that require a large number of training signals. Through the simulations, we verify that, because of its low training overhead, the proposed estimation technique can provide a higher effective spectral efficiency than that of existing channel estimation methods requiring high training overhead.