A sophisticated characterisation of a porous material structure has been challenging in material science. Three-dimensional (3D) structure analysis allows the evaluation of a material’s homogeneity, pore size distribution and pore wall properties. Micro-computed tomography (micro-CT) offers a non-destructive test method for material evaluation. This paper characterises a novel ternary binder’s porous structure using micro-CT. Gypsum–cement–pozzolan (GCP) ternary binders are low-carbon footprint binders. Both natural and industrial gypsum were evaluated as a major components of GCP binders. Porous GCP binder was obtained by a foaming admixture, and the bulk density of the material characterised ranged from 387 to 700 kg/m3. Micro-CT results indicate that pores in the range from 0.017 to 3.0 mm can be effectively detected and described for porous GCP binders. The GCP binder structure proved to be dominant by 0.1 to 0.2 mm micropores. For GCP binders produced with natural gypsum, macropores from 2.2 to 2.9 mm are formed, while GCP binders with phosphogypsum possess pores from 0.2 to 0.6 mm. Micro-CT proved to be an effective instrument for characterising the homogeneity and hierarchical pore structure of porous ternary binders.