Electronic spectrum of organoimide derivatives of hexamolybdates have first been calculated within the time-dependent density-functional theory in conjunction with Van Leeuwen-Baerends (LB94) exchange correlation potential, statistical average of orbital potentials (SAOP), and gradient-regulated connection potential (GRAC), respectively. The GRAC yields much better agreement with experiments for the excitation energies comparing with both LB94 and SAOP. The analysis of transition nature indicates that there is a significant difference between the diagonal and the orthogonal substituted derivatives. The static and dynamic third-order polarizabilities are calculated using time-dependent density-functional theory combined with the sum-over-states method. The results show that these derivatives possess remarkable large molecular third-order polarizabilities, especially for system 8 with -17882.6 x 10(-36) esu. This value is about 250 times that for the C(60) molecule. Adding the organoimide segment to the [Mo(6)O(19)](2-) can substantially increase the nu value. This variation can be traced to the different electronic transition characteristics between the derivatives of [Mo(6)O(19)](2-) and [Mo(6)O(19)](2-). For our studied systems, increasing the conjugation length and diagonal substituted are efficient ways to enhance the third-order polarizability. Thus, the organoimide derivatives of hexamolybdates may comprise a new promising class of nonlinear optical materials from the standpoint of large values, small dispersion behavior, and high transparency.