Natural gas hydrate is considered to be a promising future energy resource; therefore, obtaining its physical properties is crucial for evaluating gas production efficiency and developing reasonable exploitation strategies. In this study, we present a novel pore-scale 3D morphological modeling algorithm considering various saturation and occurrences (cementing and pore-filling) of hydrate in sediments. To evaluate the performance of the presented algorithm, 14 hydrate-bearing sediment models were constructed based on X-ray computed tomographic images of a consolidated sandy specimen under an effective stress of 3 MPa. Morphologically, the new algorithm generated pore-scale hydrate occurrences coincide with published morphological behaviors of hydrate observed via computed tomography. The tortuosity and fractal dimension of pore spaces of these models were then characterized. The pore networks are also extracted, based on which the evolution of the pore characteristics including the distributions of pore radius, throat radius, throat length, and the coordination number were investigated. Using these generated models, simulations of permeability, thermal conductivity, and electrical conductivity were conducted to evaluate the influences of hydrate saturation and occurrence. These results are validated against published data, demonstrating that this algorithm could be an effective way to construct digital hydrate-bearing sediment models using a single set of computed tomographic images of a hydrate-free specimen. This new method can also be significant for the physical evaluation of natural cores in which hydrate has dissociated during core recovering and transferring.