A driving support device for a vehicle includes a hand-off determination unit configured to determine whether or not a specific condition is satisfied, the specific condition being a condition that a steering wheel is regarded as not being operated by a driver, a support interruption unit configured to interrupt a lane departure prevention support control when the hand-off determination unit determines that the specific condition is satisfied, a vehicle speed detection unit configured to detect a vehicle speed, and a vehicle speed response processing unit configured to control whether the support interruption unit interrupts the lane departure prevention support control based on the vehicle speed.