Tool edge radius plays a significant role in affecting the surface integrity of machined products. The vast majority of existing research, however, takes no account of the effect of tool edge radius in the evaluation and modeling of machined surface roughness, an essential indicator of surface integrity. The present study fills this important research gap and has performed a total of 45 turning experiments on Unified Numbering System (UNS) A92024-T351 aluminum alloy with carefully selected cutting tools with three levels of tool edge radii. This article describes the experimental setup and measurements of tool edge radius and machined surface roughness. Machined surface roughness was evaluated using five parameters, including average roughness, root-mean-square roughness, peak roughness, maximum roughness height, and five-point average roughness. The experimental evidence presented in this article shows that the tool edge radius has a profound effect on machined surface roughness, cutting forces, and cutting vibrations. Based on the experimental data, three types of predictive models are developed, including a multiple regression model, multilayer perceptron neural network model, and radial basis function neural network model. The prediction accuracy of the three models is compared based on average mean squared errors. The results show that different models lead to different prediction accuracy for different surface roughness parameters.