The model of interdependent network based on positive/negative correlation of the degree is constructed by the typical Barabási-Albert network in this paper. Dependency modality and dependency degree are considered in the model. Two parameters F and K are defined, which represent the proportion of dependency node and the redundancy of dependency, respectively. We study the influences of different values of F and K on the robustness of interdependent network in cascading failures under degree-based attacks and random attacks and also compare the results with those from the random interdependent network model. The simulation results show that the robustness of both random independency and interdependent network based on positive/negative correlation of the degree decreases as F increases and increases as K increases; in the model of full interdependence (F = 1), the robustness of interdependent network based on positive correlation of the degree is optimal under random attacks; the interdependent network based on negative correlation of the degree shows stronger robustness in the model of partial interdependence (F= 0.2, 0.5, 0.8). While the interdependent network based on positive correlation of the degree shows poorer robustness with any value of F under degree-based attacks.