The primary purpose of this study was to investigate the feasibility of applying polymeric cementitious materials to three-dimensional additive construction (3DAC). Specifically, styrene–butadiene rubber (SBR) latex was employed as an admixture to produce SBR-modified cementitious mixtures, and their fresh properties were experimentally investigated to determine the feasibility of their use in the 3DAC process. The SBR/cement ratio was controlled based on four main materials (i.e., cement, sand, silica fume, and fly ash) in order to determine the optimal fresh properties. The test results revealed that the SBR-modified cementitious mixtures showed excellent flowability, extrudability, buildability, and open time, all of which are required for 3DAC materials. The optimal flow of the SBR-modified cementitious mixtures was 70% ± 1%, which is appropriate for 3DAC applications. According to the experiment results, the SBR-modified cementitious mixtures were sufficiently competitive to serve as a new class of materials for 3D additive construction.