This paper investigates numerically the deep renovation of a multi-family building in Greece to reduce dramatically its energy demand and also to incorporate renewable energy sources, rendering it a positive one; thus in position on an annual basis to offer net electricity to the grid. The examined building has 8 apartments of 75 m2 floor area each and is located in Moschato, a suburb of Athens in Greece. The goal of the present investigation is to determine the energy savings, but also to calculate the financial and environmental benefits through a life cycle analysis. The energy simulation of the building is conducted on annual basis by using a novel and detailed dynamic software tool (INTEMA.building), which is developed in the Dymola environment using the Modelica modeling language. This tool makes possible the detailed simulation of both passive and active systems in the building environment. Furthermore, it includes the control of the energy systems and can provide accurate enough results, encompassing detailed numerical models for the systems investigated, accounting for an adjustable time step of the dynamic analysis. According to the calculations, the proposed retrofitting scenario can achieve a reduction of the heating loads by 93% and of cooling loads by 78% respectively. The electrical demand for domestic hot water can be decreased by about 79%, while the electricity demand for appliances and lighting by about 60%. In terms of specific thermal needs, the specific heating demand can be reduced from 151.5 kWh/m2 down to 10.7 kWh/m2, while the cooling specific demand from 112.6 kWh/m2 to 24.4 kWh/m2. Moreover, it is calculated that the reduction in the primary energy demand after the renovation can be up to 88%, with the building providing around 5.3 MWh of net electricity to the grid on a yearly basis through a net-metering connection. Finally, the life cycle cost analysis indicated 622 k€ savings and specific CO2 avoidance per renovated floor area in the range of 2.64 tons CO2/m2.