Advances in deep learning have highlighted the need for models tailored for deployment in resource-constrained environments (RCEs), where memory and processing limitations present significant challenges, such as those found in mobile devices, Internet of things (IOT) devices, and embedded systems. This paper introduces GRMobiNet, a novel deep neural network (DNN) model designed to address these challenges in image classification tasks by balancing computational complexity with model accuracy in RCE settings. The model focuses on key performance goals inspired by previous state-of-the-art models, aiming to achieve a better balance between complexity and accuracy. These goals include reducing the model's computational complexity to fewer than 4 million parameters, limiting memory usage to under 16 megabytes, and achieving an accuracy greater than 80%. By meeting these objectives, GRMobiNet enhances both the effectiveness and efficiency of deep neural network deployment in RCE settings. GRMobiNet builds upon MobileNet as its baseline, incorporating advanced techniques such as depthwise separable convolutions, compound scaling, global average pooling, and quantization to optimize performance. Trained on ImageNet-10, a subset of ImageNet-1K, the model underwent rigorous performance evaluation. Experimental results demonstrate that GRMobiNet achieves its performance objectives, with a computational complexity of 3.2 million parameters, memory utilization of 12.6 megabytes, and a prediction accuracy of 92%, validating its suitability for RCEs. This research presents a scalable framework for balancing accuracy and computational efficiency, with significant implications for RCE devices. In future work, GRMobiNet will be tested on commercially available RCE mobile devices using real-world images to assess its practicality and evaluate its performance in terms of accuracy, confidence, and inference time for image classification in real-world scenarios.