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We compute the Donaldson-Thomas invariants for two types of Calabi-Yau 3-folds. These invariants are associated to the moduli spaces of rank-2 Gieseker semistable sheaves. None of the sheaves are locally free, and their double duals are locally free stable sheaves investigated earlier in [12, 25, 33] . We show that these Gieseker moduli spaces are isomorphic to some Quot-schemes. We prove a formula for Behrend's ν-functions when torus actions present with positive dimensional fixed point sets,doi:10.4310/cag.2013.v21.n3.a4 fatcat:mxkyk7cxh5h3haynpxlho2pmr4