Gaussian smoothing (GS) is a spatial low pass filtering method widely used in neuroimaging preprocessing. Full width at half maximum (FWHM) is a common parameter when the imaging data convolved with GS kernel. The convolutional neural networks (CNNs) can be considered as the feature extractor, which is implemented by applying a series of different filters. However, the influence of kernel size of GS for feature extraction remains unclear. In this study, we describe an automatic AD classification algorithm that is built on a pre-trained CNN model, AlexNet for feature extraction and support vector machine (SVM) for classification. The algorithm was trained and tested using the structural Magnetic Resonance Imaging (sMRI) data from Alzheimer's Disease Neuroimaging Initiative (ADNI). The data used in this study include 191 Alzheimer's disease (AD) patients and 103 normal control (NC) subjects. We evaluate the influence of FWHM on classification performance. When FWHM is 0mm, the classification accuracy obtained the highest value for AD and NC, which reached 91.5%, 92.4%, 89.0% for conv3, conv4 and conv5 of AlexNet respectively. The classification accuracy at each layer is relatively low when FWHM is 8mm. The result suggests that the higher smooth value may have a negative effect on feature extraction of CNNs during AD classification.