Star classification is an important topic in astronomy. For the classification of the massive high-dimensional stellar spectral data that has been collected, the pattern matching method is more successful for spectral classification, but its disadvantage is that the differences between standard star templates cannot be reflected in matching actual observed data. Especially when it comes to the classification of both spectral types and luminosity types, the template matching method often fails. Moreover, the classification of luminosity types based on spectral feature measurement strongly depends on the accuracy of spectral fitting. In order to solve the problem of classification based on spectral type and luminosity type, a Classification model of Stellar Spectral type and Luminosity type based on Convolution Neural Network (CSSL_CNN) is introduced. This model uses a convolutional network to extract features of the spectra, adds attention blocks to focus on learning important features, uses a pooling operation for dimensionality reduction, compressing the number of parameters of the model, and the fully connected layer is used to learn features and classify stars. The Large Sky Area Multi-Object Fiber Spectroscopy Telescope (LAMOST) public data set Data Release 5 (DR5) was used in the experiment to verify and evaluate the performance of the model. We used 71282 spectra from DR5, and each spectrum contains more than 3000 features. The experimental results show that the accuracy of our model reaches 92.04% in classification of spectral types, while a Celestial bodies Spectral Classification Model (CSC_Model) based on the deep neural network only reaches 87.54%, and the accuracy of our model is 83.91% in binary classification of spectral and luminosity types, while MKCLASS, a pattern matching method, only has the accuracy of 38.38%, and its efficiency is much lower.