Smart grid is expected to support electric vehicles parking lots with the existing power line infrastructure. In order to support all electric-vehicles (EVs) users to complete their charging needs before leaving the parking lot, the power grid requires that the charging demands of EVs should be within the allowable power limit to avoid the grid overloading. This paper proposes a fuzzy logic inference based algorithm (FLIA) to manage the available power efficiently for EVs in the parking lot. The problem is mathematically formulated and solved by the credibility of the fuzzy inference mechanism to control charging and discharging of the EVs. The key idea is to introduce the fuzzy inference mechanism that evaluates several uncertain input parameters from the electric grid and from EVs to obtain an adequately accurate charging or discharging decision for each of the connected EVs. The proposed scheme is applied to a parking lot with different parking capacities and compared with the conventional-based systems. The simulation results demonstrated the feasibility and effectiveness of the proposed algorithm when dealing with the available power management and satisfying the EV user's requirements.