High fluidity concrete exhibits an excellent self-compacting property. However, the application of typical high-fluidity concrete is limited in the normal strength range (18~35 MPa) due to the large amount of binder. Therefore, it is important to solve these problems by adding a viscosity modifying agent (VMA) with a superplasticizer (PCE), which helps to improve the fluidity of the concrete. In addition, the rheology and stability of the concrete with VMA can be improved by preventing bleeding and segregation issues. Current studies focused on the physical phenomena of concrete such as the fluidity, rheological properties, and compressive strength of normal-strength, high-fluidity concrete (NSHFC) with different types of a polycarboxylate-based superplasticizer (NPCE). The obtained results suggested that the combinations of all-in-one polycarboxylate-based superplasticizers (NPCE) did not cause any cohesion or sedimentation even stored for a long time. The combination of three types of VMA showed the best fluidity (initial slump flow of 595~630 mm) without any segregation and bleeding, and the compressive strength at 28 days was also found to be the highest: 34–37 MPa. From these results, the combination of PCE (2.0%) + HPMC (0.3%) + WG (0.1%) + ST (0.1%) showed an 18% higher plastic viscosity and -4.4% lower yield stress than Plain.