A multiple-input multiple-output (MIMO) wireless communication system combined with the orthogonal frequency division multiplexing (OFDM) modulation technique can mitigate the effects of multipath fading and achieve reliable high data rate transmission over broadband wireless channels. Pilots-assisted channel estimation is essential in many MIMO-OFDM systems as it enables the receiver to acquire the channel knowledge which is necessary by signal detection. Among many channel estimation algorithms. Compressed Sensing (CS) can achieve higher accuracy using a small number of pilots than that of conventional interpolation based methods. However, due to its large-sized measurement matrix, CS suffers from highly computational complexity, making it difficult to apply in many practical scenarios. Therefore, the purpose of this research is to reduce the complexity for CS based channel estimation in MIMO-OFDM systems. To this end, this thesis uses the same measurement matrices for all links in MIMO systems because the pilot arrangements for all the links are the same. In addition, for multiple antenna systems, typically the position of channel impulse response (CIR) in the time domain are almost same. Therefore, we used an average process to reduce the AWGN noise component to find the correct positions of CIR which its vital for CS based channel estimation. We selected randomly small number of pilots in order to further reduce the complexity. The simulation results showed that our proposed method provides a good bit error rate (BER) performance for the channel estimation. Furthermore, our proposed CS method reduces computational complexity by up to 75%.