The excellent dielectric properties and metal substitutability of engineering plastics make them popular for 5G construction. The detection and characterization of several engineering plastics with similar appearances but different properties can help engineering plastics be better used in manufacturing 5G circuit boards and antenna modules. The terahertz time-domain spectroscopy detection technique (THz-TDS) was applied to spectroscopically detect several common engineering plastics, PEEK, PPS, and ABS, and the terahertz time-domain spectra of three engineering plastics were obtained. The terahertz frequency domain spectra of engineering plastics at 0.1~1.2 THz were obtained by fast Fourier transform of the terahertz time-domain spectra of the three engineering plastics. The related optical parameters were extracted to obtain the terahertz absorption spectra of engineering plastics. Analysis of the THz time-domain spectra shows that the THz time-domain spectra of different kinds of engineering plastics have differences in time delay lines and amplitudes, which can visually demonstrate the differences between various classes of plastics, indicating that THz-TDS is feasible for the classification and identification of engineering plastics. However, since the same engineering plastics exhibit similar peak positions and peaks in the terahertz band and no obvious THz characteristic absorption peaks for each material, they cannot be directly determined by fingerprint spectra. Based on this, the feasibility of applying a nonlinear instrumental convolutional neural network (CNN) to the study of engineering plastics without obvious feature absorption peaks is explored. An improved CNN classification model is proposed by optimizing the network structure and important weight parameters of CNN. The model uses the LeakyRelu activation function, adds BN layers, and utilizes the Adams gradient descent algorithm, which enables to ensure the robustness of the classifier, accelerates the network classification speed and improves the accuracy of THz spectrum recognition while solving the problem of easily falling into local optimum due to the insufficient amount of THz spectrum data, and compare this method with the traditional linear tool principal component analysis-support vector machine method (PCA-SVM). Validation experiments are conducted to verify the advantages and disadvantages of the two qualitative analysis models. The experiments show that the improved CNN classification model takes 0.15 ms to run on average, with 99.6% accuracy in the training set and 98.8% accuracy in the test set; compared with the traditional PCA-SVM classification model, its classification is significantly improved, and the classification accuracy is increased by 27.3% in the test set and 30.9% in the training set. The results show that the combination of THz-TDS and the improved CNN classification model can achieve accurate identification and classification recognition of the above three engineering plastics, which provides a new method for non-contact rapid non-destructive detection and identification of engineering plastics and can also be used as a reference for the identification and detection of other substances without THz characteristic peaks.