MORUS is a third-round CAESAR candidate of authenticated cipher designed by H. Wu et al. With a fault model, the diffusion property of MORUS is analyzed in this paper. By using a bit-oriented random fault model, the search algorithm for the differential chain of MORUS is improved with the usage of differential analysis and meet-in-the-middle technique. Through this algorithm, a 5-step differential chain is discovered with a probability of 2^-85. The differential-distinguish attack on the initialization of 5-step reduced version of MORUS-640-128 is proposed with the data complexity of 2⁸⁹ and the distinguishing advantage of 0.99965. By using differential fault analysis method, the forgery attack on 3-step authentication of MORUS-640-128 is formed.