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This paper describes a three-dimensional (3D) visualization framework using terahertz (THz) waves for quantitative analysis of the distribution of catalyst washcoat loading and diesel particulate filter (DPF) soot deposits. THz waves, which are electromagnetic waves located between infrared and microwave in the electromagnetic spectrum, have good directivity and moderate resolution. Accordingly, a computed tomography (CT) technique has been developed to image the interior of an object using the spectral information of THz waves. This THz wave CT technique can be used to analyze the interior of various target objects, and has good penetrability of ceramic substances used as catalysts in automobiles. Against this background, a method using THz CT for nondestructive analysis of catalyst washcoat loading and the density distribution of soot was developed, and this framework was evaluated.