An LED drive device whose power dissipation can be effectively reduced without halting current supply to an LED row as well as an LED illuminating device with the LED drive device incorporated therein. When an LED 21A making up an LED row 3A has developed a short-circuit fault, a voltage corresponding to a forward voltage which has been applied to the faulty LED 21A is impressed additionally to an FET 31A for electric power consumption thereof to increase to not less than a certain value. At this time, a power limiting circuit 6A varies a potential, being a reference value of a constant current circuit 7A, at a connecting point between voltage dividing resistors 46A, 47A and then continues to supply a certain level of a current IF1 to the LED row 3A so as to keep the remaining fault-free LEDs 22A to 26A lighting. Consequently, in the event of a short-circuit fault of the LED 21A, the adverse effect caused by discontinuing the current supply to the LED row 3A can be swept away.