A sensorless measurement device for filter capacitor current by using a state observer is provided. The sensorless measurement device comprises a chip, wherein the chip comprises the state observer. The state observer is configured to retrieve a filter-capacitor-voltage actual value and a direct current link (dc-link) voltage of a present sampling time. According to the filter-capacitor-voltage actual value and the dc-link voltage, the state observer is configured to output a filter-capacitor-voltage state variable value, a filter-capacitor-current state variable value, and a disturbance-voltage state variable value of a next sampling time. The filter-capacitor-current state variable value is an average current value without ripples.