We address pilot-aided channel estimation for a flat-fading spatially-correlated MIMO system, which employing Uniform Linear Arrays (ULA) on dual side and working in sparse scattering (multipath) environment. In case of sparse scattering, channel matrix and spatial correlation of flat-fading MIMO systems are parameterized by structure of multipaths, which is represented as Direction of Arrivals (DOAs), Direction of Departures (DODs) and complex path fading of each path. Based on this and block-fading property of channel, we design a channel estimation method via estimating multipath parameters using ESPRIT-like DOA-Matrix method which exploits shift-invariance property of ULA. The proposed method is able to obtain improved Mean-Square-Error performance than Least-Square method without prior information of spatial correlation.