Recently, a hyperspectral imaging system (HIS) with a Fourier Transform InfraRed (FTIR) spectrometer has been widely used due to its strengths in detecting gaseous fumes. Even though numerous algorithms for detecting gaseous fumes have already been studied, it is still difficult to detect target gases properly because of atmospheric interference substances and unclear characteristics of low concentration gases. In this paper, we propose detection algorithms for classifying hazardous gases using a deep neural network (DNN) and a convolutional neural network (CNN). In both the DNN and CNN, spectral signal preprocessing, e.g., offset, noise, and baseline removal, are carried out. In the DNN algorithm, the preprocessed spectral signals are used as feature maps of the DNN with five layers, and it is trained by a stochastic gradient descent (SGD) algorithm (50 batch size) and dropout regularization (0.7 ratio). In the CNN algorithm, preprocessed spectral signals are trained with 1 × 3 convolution layers and 1 × 2 max-pooling layers. As a result, the proposed algorithms improve the classification accuracy rate by 1.5% over the existing support vector machine (SVM) algorithm for detecting and classifying hazardous gases.