MDS matrices are used as linear diffusion layer in symmetric cryptography, and provide better resistance to differential and linear attack. Lighter MDS matrices can lead to cheaper implementations both in softwares and hardwares. Many researchers are devoted to searching lighter MDS matrices in recent years [Y. Li, M.S. Wang. On the construction of lightweight circulant involutory MDS matrices. FSE 2016].MDS matrices are important parts for block ciphers. We searched the $4\times 4$ MDS matrices over GL(4, $\F_2$), and found the lightest MDS matrices only have 10 XOR operations. Besides, all these lightest MDS matrices can be classified to 3 classes.