Alzheimer's Disease (AD) is a progressive condition of a neurological brain disorder recognized by symptoms such as dementia, memory loss, alterations in behaviour, and impaired reasoning abilities. Recently, many researchers have been working to develop an effective AD recognition system using deep learning (DL) based convolutional neural network (CNN) model aiming to deploy the automatic medical image diagnosis system. The existing system is still facing difficulties in achieving satisfactory performance in terms of accuracy and efficiency because of the lack of feature ineffectiveness. This study proposes a lightweight Stacked Convolutional Neural Network with a Channel Attention Network (SCCAN) for MRI based on AD classification to overcome the challenges. In the procedure, we sequentially integrate 5 CNN modules, which form a stack CNN aiming to generate a hierarchical understanding of features through multi-level extraction, effectively reducing noise and enhancing the weight's efficacy. This feature is then fed into a channel attention module to select the practical features based on the channel dimension, facilitating the selection of influential features. . Consequently, the model exhibits reduced parameters, making it suitable for training on smaller datasets. Addressing the class imbalance in the Kaggle MRI dataset, a balanced distribution of samples among classes is emphasized. Extensive experiments of the proposed model with the ADNI1 Complete 1Yr 1.5T, Kaggle, and OASIS-1 datasets showed 99.58%, 99.22%, and 99.70% accuracy, respectively. The proposed model's high performance surpassed state-of-the-art (SOTA) models and proved its excellence as a significant advancement in AD classification using MRI images.