In this paper, the induced continuous ordered weighted averaging (IC-OWA) operator is obtained by combining the induced ordered weighted averaging (IOWA) operator and the continuous interval argument ordered weighted averaging (C-OWA) operator and some characteristecs are studied. Based on the interval number complementary judgment matrix, the interval continuous multiplicative preference matrix is proposed and the induced continous ordered weighted averaging (DIC-OWA) operator is defined on the basis of the deviation of assessment level of experts. A method of interval number multi-attribute group decision making based on the DIC-OWA operator is proposed. Finally, an illustrative example is given and the results show that the method is feasible.