An engine control unit comprising: an idling-stop controller to automatically stop an engine equipped in a vehicle if a coasting-state idling-stop condition or a stationary-state idling-stop condition is satisfied, the coasting-state idling-stop condition including a coasting-state of the vehicle at a speed (V 1) or lower, the stationary-state idling-stop condition including a stationary-state of the vehicle; an idling-start controller to restart the engine if a restart condition is satisfied during an automatic stop of the engine by the idling-stop controller; a diagnoser to find, during the automatic stop of the engine or a restart of the engine, some abnormality in devices operating during an automatic stop of the engine or the restart of the engine; and a road-grade acquirer to acquire a road-grade (θ) at the location of the vehicle, characterized in that the coasting-state idling-stop condition includes the road-grade (θ) acquired by the road-grade acquirer being not higher than a first coasting-state road-grade (θ PC1) before an initial automatic stop of the engine by the idling-stop controller, the coasting-state idling-stop condition includes the road-grade (θ) acquired by the road-grade acquirer being not higher than a second coasting-state road-grade (θ PC2) higher than the first coasting-state road-grade (θ PC1), after the initial automatic stop of the engine by the idling-stop controller, the stationary-state idling-stop condition includes the road-grade (θ) acquired by the road-grade acquirer being not higher than a first stationary-state road-grade (θ PS1) higher than the first coasting-state road-grade (θ PC1), before the initial automatic stop of the engine by the idling-stop controller, the stationary-state idling-stop condition includes the road-grade (θ) acquired by the road-grade acquirer being not higher than a second stationary-state road-grade (θ PS2) higher than the first stationary-state road-grade (θ PS1), after the initial automatic stop of the engine by the idling-stop controller, the road-grade acquirer acquires a road-grade (θ) estimated based on a longitudinal acceleration (α S) of the vehicle in a stationary-state, and acquires a road-grade (θ) estimated based on the longitudinal acceleration (α S) of the vehicle and another acceleration (α V) of the vehicle in a running-state, and the idling-stop controller inhibits an automatic stop of the engine if the diagnoser finds some abnormality in the devices operating during an automatic stop of the engine or a restart of the engine. an idling-stop controller to automatically stop an engine equipped in a vehicle if a coasting-state idling-stop condition or a stationary-state idling-stop condition is satisfied, the coasting-state idling-stop condition including a coasting-state of the vehicle at a speed (V 1) or lower, the stationary-state idling-stop condition including a stationary-state of the vehicle; an idling-start controller to restart the engine if a restart condition is satisfied during an automatic stop of the engine by the idling-stop controller; a diagnoser to find, during the automatic stop of the engine or a restart of the engine, some abnormality in devices operating during an automatic stop of the engine or the restart of the engine; and a road-grade acquirer to acquire a road-grade (θ) at the location of the vehicle, characterized in that the coasting-state idling-stop condition includes the road-grade (θ) acquired by the road-grade acquirer being not higher than a first coasting-state road-grade (θ PC1) before an initial automatic stop of the engine by the idling-stop controller, the coasting-state idling-stop condition includes the road-grade (θ) acquired by the road-grade acquirer being not higher than a second coasting-state road-grade (θ PC2) higher than the first coasting-state road-grade (θ PC1), after the initial automatic stop of the engine by the idling-stop controller, the stationary-state idling-stop condition includes the road-grade (θ) acquired by the road-grade acquirer being not higher than a first stationary-state road-grade (θ PS1) higher than the first coasting-state road-grade (θ PC1), before the initial automatic stop of the engine by the idling-stop controller, the stationary-state idling-stop condition includes the road-grade (θ) acquired by the road-grade acquirer being not higher than a second stationary-state road-grade (θ PS2) higher than the first stationary-state road-grade (θ PS1), after the initial automatic stop of the engine by the idling-stop controller, the road-grade acquirer acquires a road-grade (θ) estimated based on a longitudinal acceleration (α S) of the vehicle in a stationary-state, and acquires a road-grade (θ) estimated based on the longitudinal acceleration (α S) of the vehicle and another acceleration (α V) of the vehicle in a running-state, and the idling-stop controller inhibits an automatic stop of the engine if the diagnoser finds some abnormality in the devices operating during an automatic stop of the engine or a restart of the engine.