The double and triple tuned filters have the advantages of occupying less space， cutting down the number of high voltage capacitors， reactors and breakers， etc.， and have been widely used in HVDC projects. However， when damped type multi-tuned filters in existence are used for low order harmonic filtering， there will be much more power loss at fundamental frequency. This paper introduces a new damped type double and triple tuned filter circuits with less power loss. The invention lets some L and C components of the filter form a series tuned circuit at fundamental frequency， which is connected in parallel with a damping resister， so as to avoid the power loss on the resistor at fundamental frequency. New filters are costless in operation when used in HVDC power transmission system.