We theoretically study the high-order harmonic generation and attosecond pulse generation of CO molecule exposed to a two-color combined field composed of 800 nm and 2000 nm laser pulses based on the strong field approximation, where the effect of linear Stark shift on molecular energy levels is considered. The two-color combined field can be efficiently controlled by optimizing their relative carrier envelope phases. The results show that the cut-off of harmonics is significantly extended in the combined field, and the supercontinuum of harmonics is apparently improved due to the ionization suppression of asymmetric molecule in a certain direction, which leads to the decrease of quantum interference during the propagation of the continuum electron. By superimposing several harmonics of the plateau region, the isolated attosecond pulse can be obtained for several relative phases, and the shortest pulse achieves 98 as. The width of attosecond pulse is obviously shortened compared with the situation that CO molecule is driven by a one-color laser field.