Three-dimensional printed concrete (3DPC) is a relatively recent technology that may be very important in changing the traditional construction industry. The principal advantages of its use are more rapid construction, lower production costs, and less residues, among others. The choice of raw materials to obtain adequate behavior is more critical than for traditional concrete. In the present paper a mixture of cement, silica fume, superplasticizer, setting accelerator, filler materials, and aggregates was studied to obtain a 3DPC with high resistance at short curing times. When the optimal mixture was found, metallic fibers were introduced to enhance the mechanical properties. The fresh and hard properties of the concrete were analyzed, measuring the setting time, workability, and flexural and compressive strength. The results obtained demonstrated that the incorporation of fibers (2% in volume) enhanced the flexural and compressive strength by around 163 and 142%, respectively, compared with the mixture without fibers, at 9 h of curing. At 28 days of curing, the improvement was 79.2 and 34.7% for flexural and compressive strength, respectively.