A structure for operating a system for utilizing exhaust heat of a vehicle may include a high-temperature part with an exhaust pipe and a bypass passage installed in the exhaust pipe, a thermoelectric element attached to an exterior of the exhaust pipe for generating electricity, a low-temperature part attached to an exterior of the thermoelectric element for flowing a coolant, a first exhaust gas passage installed in the low-temperature part and having both ends connected to the exhaust pipe, a first valve to selectively open or close the first exhaust gas passage, a second exhaust gas passage formed in a space between the inner circumferential surface of the exhaust pipe and an outer circumferential surface of the bypass passage, a second valve disposed at a rear end of the bypass passage, coupled to a valve shaft and rotatable on the basis of the valve shaft, and an operating unit.