Studies have indicated that reducing the process energy demand is as important as improving the energy conversion efficiency to make manufacturing equipment more energy efficient. However, little work has been done to understand the energy demand characteristics of the widely employed drawing process. In this paper, the energy demand of the cylindrical drawing process under a range of operating parameters was measured and analyzed. Since any energy saving efforts should not have negative effects on the product quality, the forming quality of the drawn part indicated by the maximum thinning and thickening ratios and variation of thickness was also considered. To identify the main contributors to energy demand and forming quality, two sets of experiments were designed based on the Taguchi method. The first set of experiments include three parameters (i.e., punch velocity, blank holder force, and drawn depth) at three levels, while the second set of experiments only include two factors (i.e., punch velocity and blank holder force) at three levels due to their impacts on the forming quality. Analysis of variance (ANOVA) and analysis of means (ANOM) were then used to analyze the experimental results. Finally, grey relational analysis (GRA) was used to reveal the correlation between the forming quality and the process energy. Results show that the mean thickness variation has the strongest relational grading with the process energy, which suggests that the process energy can be used as an effective indicator to predict mean thickness variation of the drawn part. The identified characteristics of the process energy and the forming quality can be used to select process parameters for reduced energy demands of drawing processes.