This paper presents an automatic classification of plastic material’s inorganic pigment using terahertz spectroscopy and convolutional neural networks (CNN). The plastic materials were placed between the THz transmitter and receiver, and the acquired THz signals were classified using a supervised learning approach. A THz frequency band between 0.1–1.2 THz produced a one-dimensional (1D) vector that is almost impossible to classify directly using supervised learning. This paper proposes a novel pre-processing of 1D THz data that transforms 1D data into 2D data, which are processed efficiently using a convolutional neural network. The proposed pre-processing algorithm consists of four steps: peak detection, envelope extraction, and a down-sampling procedure. The last main step introduces the windowing with spectrum dilatation that reorders 1D data into 2D data that can be considered as an image. The spectrum dilation techniques ensure the classifier’s robustness by suppressing measurement bias, reducing the complexity of the THz dataset with negligible loss of accuracy, and speeding up the network classification. The experimental results showed that the proposed approach achieved high accuracy using a CNN classifier, and outperforms 1D classification of THz data using support vector machine, naive Bayes, and other popular classification algorithms.