In this thesis, an innovative system of floor and roof construction has been developed; employing open web steel joists and pre-cast concrete floor panels that joins together by small amount of cast in place concrete is the main objective to set-up a lightweight, easy to erection and cost-effective floor system. The proposed system designed in a way that it has advantages of both prefabricated and composite construction. First in this research and as a real example, the proposed system was designed for a floor of an office building. Then a computer program was developed in MATLAB environment to optimize the cost and weight of the floor system for two loading conditions (live loads in office and residential buildings), spans and floor depths. The computer model uses several parameters in design calculations such as required steel sections for the bottom and top chords of steel joist, lenth of concrete panels (proportioned to joist spacing) and the required I sections for girders. Finally, result of calculations integrated into several tables and lightest and cheapest floor systems for different loadings and geometrical conditions has been indicated. Calculations showed that using of the proposed floor system can reduce the total dead weight of the floors up to 65 or 70 percent in comparison with the current block and joist system that uses in Iran .