This paper aims to develop a new deep learning model (DeepPneuNet) and evaluate its performance in predicting Pneumonia infection diagnosis based on patients' chest x-ray images. We have collected 5856 chest x-ray images that are labeled as either "pneumonia" or "normal" from a public forum. Before applying the DeepPneuNet model, a necessary feature extraction and feature mapping have been done on the input images. Conv2D layers with a 1 x 1 kernel size are followed by ReLU activation functions to make up the model. These layers are in charge of recognizing important patterns and features in the images. A MaxPooling 2D procedure is applied to minimize the spatial size of the feature maps after every two Conv2D layers. The sparse categorical cross-entropy loss function trains the model, and the Adam optimizer with a learning rate of 0.001 is used to optimize it. The DeepPneuNet provides 90.12% accuracy for diagnosis of the Pneumonia infection for a set of real-life test images. With 9,445,586 parameters, the DeepPneuNet model exhibits excellent parameter efficiency. DeepPneuNet is a more lightweight and computationally efficient alternative when compared to the other pre-trained models. We have compared accuracies for predicting Pneumonia diagnosis of our proposed DeepPneuNet model with some state-of-the-art deep learning models. The proposed DeepPneuNet model is more advantageous than the existing state-of-the-art learning models for Pneumonia diagnosis with respect to accuracy, precision, recall, F-score, training parameters, and training execution time.