In this study, the fresh properties of ethylene–vinyl acetate (EVA)-modified cementitious mixtures were experimentally investigated to evaluate the feasibility of this type of material being used in additive construction by extrusion (ACE). The EVA/cement ratio was a main variable to determine the properties, including flowability, extrudability, buildability, and open time. According to the flow test results, the optimized flow of the EVA-modified cementitious mixtures was found to be 65% for buildability. This excellent flowability could be achieved because the flow increased as the EVA/cement ratio increased; conversely, the extrudability was slightly reduced when the EVA/cement ratio increased. However, if the flow of the EVA-modified cementitious mixtures was maintained at 65%, ACE could be achieved without significant issues. In addition, the height of the additive concrete walls created was not substantially reduced after printing of these mixtures, even though different EVA/cement ratios were applied. Plus, ACE can be operated longer with such mixtures because the open time becomes longer as the EVA/cement ratio increases. In summary, the results clearly demonstrated that EVA-modified cementitious mixtures were feasible for use as ACE materials.