Automatically monitoring finishing quality by computers can achieve efficient product quality management and can improve overall production efficiency. To be able to offer quantitative measures and to achieve this goal, this paper discusses and suggests the utilization of artificial intelligence (AI) technology to predict product finishing quality by use of signals such as vibrations captured by accelerometers generated during manufacturing. To reduce the cost of inspecting products one by one, a deep one-dimensional convolutional neural network (CNN) is proposed to predict machined surface quality. In this method, dense residual skip-connections are used to improve the complexity of the model to improve the accuracy of predicted values. With the adaptation of the pooling layer in the proposed model, it is observed that the number of parameters used in the model is greatly reduced. Not only the predicted accuracy is optimized with the proposed model, the parameters that need to be stored and the computation resource that is consumed in the inference stage are significantly reduced as well. Compared with methods reported in the literature, through calibrated experimental verifications, the proposed model used in this work can improve the prediction accuracy by 10 percent, without any additional signal preprocessing efforts. The work presented in this paper is thought to have engineering implications in quantifying machining quality in the machine tools industry.