Alzheimer's disease (AD) is a progressive neurodegenerative disease, and the development of AD is irreversible. However, preventive measures in the presymptomatic stage of AD can effectively slow down deterioration. Fluorodeoxyglucose positron emission tomography (FDG-PET) can detect the metabolism of glucose in patients' brains, which can help to identify changes related to AD before brain damage occurs. Machine learning is useful for early diagnosis of patients with AD using FDG-PET, but it requires a sufficiently large dataset, and it is easy for overfitting to occur in small datasets. Previous studies using machine learning for early diagnosis with FDG-PET have either involved the extraction of elaborately handcrafted features or validation on a small dataset, and few studies have explored the refined classification of early mild cognitive impairment (EMCI) and late mild cognitive impairment (LMCI). This article presents a broad network-based model for early diagnosis of AD (BLADNet) through PET imaging of the brain; this method employs a novel broad neural network to enhance the features of FDG-PET extracted via 2D CNN. BLADNet can search for information over a broad space through the addition of new BLS blocks without retraining of the whole network, thus improving the accuracy of AD classification. Experiments conducted on a dataset containing 2,298 FDG-PET images of 1,045 subjects from the ADNI database demonstrate that our methods are superior to those used in previous studies on early diagnosis of AD with FDG-PET. In particular, our methods achieved state-of-the-art results in EMCI and LMCI classification with FDG-PET.