Diabetic Retinopathy (DR) is a leading cause of vision loss among diabetic patients, necessitating effective screening and grading for timely intervention. Regular screening significantly increases the workload of ophthalmologists, and accurate grading into stages—mild, moderate, severe, and proliferative—is crucial for monitoring disease progression. While Computer-Aided Diagnosis (CAD) systems can alleviate this burden, existing Convolutional Neural Network (CNN)-based frameworks use fixed-size kernels in a linear feed-forward manner. This approach can lead to information loss in the initial stages due to limited feature utilization across adjacent layers. To address this limitation, we propose a Hierarchical Features Fusion Convolutional Neural Network (HFF-Net) within a Diabetic Retinopathy Screening and Grading (DRSG) framework. The framework includes preprocessing to extract regions of interest from fundus images (FIs), enhancement using Contrast Limited Adaptive Histogram Equalization (CLAHE), and data augmentation for class balancing and overfitting mitigation. HFF-Net extracts multiscale features that fused at multiple levels within the network, utilizing the swish activation function for improved learning stability. We evaluated HFF-Net against several state-of-the-art CNN classifiers within the DRSG framework. Experimental results demonstrate that HFF-Net achieves a grading accuracy of 73.77 %, surpassing the second-best model by 3.51 percentage points (a relative improvement of approximately 5 %), and attains a screening accuracy of 98.70 % using only 1.18 million parameters. These findings highlight HFF-Net's potential as an efficient and effective tool in CAD systems for DR screening and grading.