Soil structure plays an important role in edaphic conditions and the environment. In this study, we investigated the effects of organic amendment on soil structure and hydraulic properties. A corn field in a semiarid land was separately amended with sheep manure compost at five different rates (2, 4, 6, 8 and 10 t/ha) and corn stover (6 t/ha) in combination with two decomposing agents. The soil structure of different amended soils was analyzed from the aggregate and pore domain perspectives. The internal pore structure of the soil was visualized through X-ray computed tomography and quantified using a pore-network model. Soil aggregate-size distribution and stability, saturated hydraulic conductivity, and water-retention curves were measured by sampling or in situ. The gas permeability and diffusivity of different amended soils were simulated based on the extracted pore networks. The aggregate stability of the amended soils was improved compared with the control, that is, the mean weight diameter increased and the percentage of aggregate destruction decreased. The stability of soil aggregates varied non-monotonically with the application rate of compost and decreased after treatment with corn stover and decomposing agents. The pore-network parameters including air-filled porosity, pore radius, throat length, and coordinate number increased for the amended soils compared with the control. The mean pore size increased with increasing compost incorporation rate. The saturated hydraulic conductivity of the compost-amended soils was higher than that of the control but varied quadratically with the application rate. The saturated hydraulic conductivity of soil treated with corn stover and decomposing agents was clearly higher than that without the agent and the control. The greater gas diffusivity and air permeability indicate that soil aeration improved following the incorporation of organic amendments. The air permeability versus air-filled porosity relationship followed a power law, and the gas diffusivity versus air-filled porosity relationship was characterized by a generalized density-corrected model regardless of amendment. The findings of this study can help improve the understanding of soil structure and hydrological function to organic fertilizer incorporation and further monitor the quality of soil structure through the pore space perspective.