In this work, we present a detailed investigation of the influences of intrinsic spin-orbit coupling (ISOC) as well as Rashba spin-orbit coupling (RSOC) on thermoelectric properties of molybdenum disulfide nanoribbons with armchair and zigzag edges, theoretically. For this purpose, we generalize the tight-binding model including the effects of the ISOC on all the atoms and a RSOC induced by a vertical electric field. By the calculation of the quantum spin-dependent transmission function from the recursive non-equilibrium Green's function model using the multi-band Slater-Koster tight-binding method, the electrical and thermal currents flowing to the right lead can be obtained from the Landauer-Buttiker formulae. Hence, the temperature-dependent electrical conductance (G), the thermal conductivity the Seebeck thermopower (S), and the thermoelectric efficiency (ZT) are discussed. The results predict a noticeable semiconducting behavior with n type, which exhibits a linear temperature dependence of the gap energy for both nanoribbons. The predicted ZT values demonstrate that the nanoribbons can be optimized to exhibit very good thermoelectric performance in which its value is not affected under influence of the electric field-induced RSOC in the ZMoS nanoribbon). Based on the used model, a large Seebeck coefficient is obtained in both types of the nanoribbons. Our results may be useful in designing novel thermoelectric devices based on two-dimensional materials as one of suitable nanoscale device.