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Classification of stellar spectra from voluminous spectra is a very important and challenging task. In order to better classify stellar spectra, inspired by the principle of deep convolutional neural network (CNN), we propose a supervised algorithm for stellar spectra classification based on 1D stellar spectra convolutional neural network (1D SSCNN). In 1D SSCNN, we modify the traditional 2D convolutional neural network into 1D network to adapt to the spectral classification. On the basis of using convolution algorithm, the spectral features are extracted and used for classification. We first use the stellar spectra data to train a 1D SSCNN to obtain a well-trained model, and then we apply the well-trained model to classify the unknown spectra. To evaluate the performance of the proposed algorithms, we apply 1D SSCNN to classify three spectral types: F-type spectra, G-type spectra, and K-type spectra and 10 subclasses of K-type spectra: A0-type, A5-type, F0-type, F5-type, G0-type, G5-type, K0-type, K5-type, M0-type, and M5-type spectra from Sloan Digital Sky Survey (SDSS). Our 1D SSCNN algorithm obtain higher classification accuracy compared with support vector machine (SVM), random forest (RF), and artificial neural network (ANN). [ABSTRACT FROM AUTHOR]