The incremental forming technique is a relatively new sheet forming process, normally used for prototype or low-quantity manufacturing of components with complicated geometries. This article is concerned with the warm incremental forming of Ti-6Al-4V titanium alloy. To reduce the time and costs involved for the investigation, on one hand, the groove test which is simple and requires small specimens is employed and, on the other hand, the experiments are designed based on the Taguchi method, which considerably reduces the number of necessary tests. With regard to this, the influence of some important process variables, namely the initial sheet temperature, tool diameter and vertical pitch, on several objective parameters such as forming limit, thickness reduction, drawing depth and the final sample temperature are studied. Based on the Taguchi and variance analyses, the rank and contribution percentage of each process variable are, respectively, determined. In all the cases, there is a good agreement between the results of these analyses. Moreover, the vertical pitch is shown to be the most effective parameter for different objective variables, excepting the final temperature where the tool diameter is the most influencing variable. The optimum test conditions based on various criteria are then specified using the Taguchi method. After conducting the practical experiments with these optimum test conditions, a very good correlation between the relevant findings and the Taguchi predictions are found.