The fully coupled conditional moment closure (CMC) modeling with an unstructured-grid finite volume method has been developed to realistically simulate the structure of complex, turbulent non-premixed syngas-air flames, where flame structures could be considerably influenced by turbulence, transport history, and heat transfer. In this study, conservative CMC formulation is used to improve robustness and accuracy in the boundary treatment of CMC-related fluxes. To correctly account for the transport effect, the CMC transport equations fully coupled with equations for the flow and mixing fields are numerically solved. Moreover, to reduce the excessive computational burden required for three-dimensional computations of the fully coupled CMC approach with detailed chemistry, parallel strategies are implemented into the general CMC formulation. The present fully coupled CMC formulation together with a parallel processing procedure successfully demonstrates the capability to realistically predict detailed structure and overall combustion characteristics in this three-dimensional turbulent non-premixed syngas flame. The numerical results obtained in this study clearly reveal the importance of convective and radiative heat transfer in modeling the precise structure and NO, emissions of a confined three-dimensional turbulent non-premixed syngas flame with a cooling wall. In dealing with physically and geometrically complex turbulent non-premixed flames encountered in practical combustors, numerical results also confirm that the present unstructured-grid approach together with the fully coupled CMC model is a viable and robust tool for geometric flexibility and to realistically represent the turbulence-chemistry interaction. A parallel procedure implemented in the unstructured-grid approach and the conservative CMC formulation greatly improves computational efficiency, especially for the solution of a three-dimensional complex turbulent non-premixed flame field with large grid number and detailed chemistry.