Early diagnosis of Alzheimer's disease and its prodromal stage, also known as mild cognitive impairment (MCI), is critical since some patients with progressive MCI will develop the disease. We propose a multi-stream deep convolutional neural network fed with patch-based imaging data to classify stable MCI and progressive MCI. First, we compare MRI images of Alzheimer's disease with cognitively normal subjects to identify distinct anatomical landmarks using a multivariate statistical test. These landmarks are then used to extract patches that are fed into the proposed multi-stream convolutional neural network to classify MRI images. Next, we train the architecture in a separate scenario using samples from Alzheimer's disease images, which are anatomically similar to the progressive MCI ones and cognitively normal images to compensate for the lack of progressive MCI training data. Finally, we transfer the trained model weights to the proposed architecture in order to fine-tune the model using progressive MCI and stable MCI data. Experimental results on the ADNI-1 dataset indicate that our method outperforms existing methods for MCI classification, with an F1-score of 85.96%.