The massive volume of grid-enabled vehicles (GEVs) following environmental compatibility has created challenges for utilities in supplying energy and maintaining load balance in the grid. A proper schedule can turn this challenge into an opportunity to modify the network load consumption curve (NLCC). Extensive research has coordinated GEVs with the network, each of which has investigated some influencing factors. These factors include the request-initiate random nature, the charging costs, the battery capacity, the initial charging, and the reduction of charge costs. In a two-way charging and discharging (C/D) system, no comprehensive study has investigated all the factors mentioned to modify the NLCC over one period. This study has offered a simple scheduling for coordinating GEVs with the network, which has accounted for the mentioned factors. In this scheduling, the NLCC averaging method has determined the C/D range in one period. The presented algorithms prioritize the GEVs information and encode it using the binary code method, control the load consumption (LC) and calculate the costs. The LC instantaneously compared with NLCC. Then the NLCC is remodified each time to get closer to the ideal state. This method has been simulated on Mazandaran NLCC and has given a favorable result.