Energy dissipation Systems in civil engineering structures are sought when it comes to removing unwanted energy such as instability, earthquake and wind. Among these systems, there is the combination of structural steel frames with passive energy dissipation provided by Fluid Viscous Dampers (FVD). This device is increasingly used to provide better seismic protection for existing as well as new buildings and bridges. A 3 D numerical investigation is done considering the seismic response of a twelve-story steel building moment frame with diagonal FVD that have linear force versus velocity behaviour. Nonlinear time history, which is being calculated by Fast nonlinear analysis (FNA), of Boumerdes earthquake (Algeria, May 2003) is considered for the analysis and carried out using the SAP2000 software and comparisons between unbraced, braced and damped structure are shown in a tabulated and graphical format. The results of the various systems are studied to compare the structural response with and without this device of the energy dissipation thus obtained were discussed. The conclusions showed the formidable potential of the FVD to improve the dissipative capacities of the structure without increasing its rigidity. It is contributing significantly to reduce the quantity of steel necessary for its general stability.