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The aggravation of left ventricular diastolic dysfunction (LVDD) could lead to ventricular remodeling, wall stiffness, reduced compliance, and progression to heart failure with a preserved ejection fraction. A non-invasive method based on convolutional neural networks (CNN) and heart sounds (HS) is presented for the early diagnosis of LVDD in this paper. A deep convolutional generative adversarial networks (DCGAN) model-based data augmentation (DA) method was proposed to expand a HS database of LVDD for model training. Firstly, the preprocessing of HS signals was performed using the improved wavelet denoising method. Secondly, the logistic regression based hidden semi-Markov model was utilized to segment HS signals, which were subsequently converted into spectrograms for DA using the short-time Fourier transform (STFT). Finally, the proposed method was compared with VGG-16, VGG-19, ResNet-18, ResNet-50, DenseNet-121, and AlexNet in terms of performance for LVDD diagnosis. The result shows that the proposed method has a reasonable performance with an accuracy of 0.987, a sensitivity of 0.986, and a specificity of 0.988, which proves the effectiveness of HS analysis for the early diagnosis of LVDD and demonstrates that the DCGAN-based DA method could effectively augment HS data.