A vehicle as a host vehicle comprising: a vehicle drive source; a preceding vehicle information acquiring device configured to acquire preceding vehicle information relating to a preceding vehicle, including a parameter relating to a distance between vehicles which becomes greater the wider the distance between the host vehicle and the preceding vehicle; and an electronic control unit configured to receive said parameter from the preceding vehicle information acquiring device and configured to control the vehicle drive source, in which vehicle, an internal combustion engine is provided as the vehicle drive source and the electronic control unit is configured to operate the internal combustion engine in an idle reduction mode, where the internal combustion engine is automatically made to stop when at least a predetermined engine stop condition is given and to automatically restart when at least a predetermined engine start condition is given; wherein the electronic control unit is further configured so that, as one of the predetermined start conditions, when the parameter becomes a first predetermined value or more during the idle reduction mode with the internal combustion engine being stopped, the internal combustion engine automatically restarts; the vehicle being characterized in that the electronic control unit is further configured so that as one of the predetermined engine stop conditions, following said previously defined engine start condition, if the host vehicle continues to be stopped when the preceding vehicle has stopped before the parameter becomes a second predetermined value larger than the first predetermined value, it again makes the internal combustion engine automatically stop. a vehicle drive source; a preceding vehicle information acquiring device configured to acquire preceding vehicle information relating to a preceding vehicle, including a parameter relating to a distance between vehicles which becomes greater the wider the distance between the host vehicle and the preceding vehicle; and an electronic control unit configured to receive said parameter from the preceding vehicle information acquiring device and configured to control the vehicle drive source, in which vehicle, an internal combustion engine is provided as the vehicle drive source and the electronic control unit is configured to operate the internal combustion engine in an idle reduction mode, where the internal combustion engine is automatically made to stop when at least a predetermined engine stop condition is given and to automatically restart when at least a predetermined engine start condition is given; wherein the electronic control unit is further configured so that, as one of the predetermined start conditions, when the parameter becomes a first predetermined value or more during the idle reduction mode with the internal combustion engine being stopped, the internal combustion engine automatically restarts; the vehicle being characterized in that the electronic control unit is further configured so that as one of the predetermined engine stop conditions, following said previously defined engine start condition, if the host vehicle continues to be stopped when the preceding vehicle has stopped before the parameter becomes a second predetermined value larger than the first predetermined value, it again makes the internal combustion engine automatically stop.