A multi-objective energy management strategy for a plus-zero energy building during a year, incorporating renewable resources, air to water heat pump, micro-CHP, ventilation, energy storage systems and thermal-cooling-electrical loads have been proposed in this paper. In this strategy, a novel technology of wind turbine that has been known as INVELOX has been investigated and collaborated in ZEB planning to reach efficient plus-ZEB at lower cost and pollution. As well the building can sell and buy power to/from the upstream network. The total cost and pollution of the building have been considered as objective functions. Also, the effect of objective function priority on the planning of the building has considered. To make the results more realistic the wind speed and solar radiation of Kermanshah city in Iran have been used. The presented problem has modeled as a mixed-integer linear programming and the Epsilon constraint method and fuzzy satisfying approach have been used to solve and obtain the best solution. The final results show reducing the total cost and pollution by about 34.6% and 51.2% in cost priority, also 28.7% and 54.7% in pollution priority respectively, also increment in surplus power to sell to the grid and getting closer to reach plus-ZEB concept