This paper introduces a novel denoising algorithm for the partial-discharge(PD) signals from power apparatuses. The developed algorithm includes three kinds of specific denoising sub-algorithms. The first sub-algorithm uses the fuzzy logic which classifies the noise types in the magnitude versus phase PD pattern. This sub-algorithm is especially effective in the rejection of the noise with high and constant magnitude. The second one is the method simply removing the pulses in the phase sections below the threshold count in the count versus phase pattern. This method is effective in removing the occasional high level noise pulses. The last denoising sub-algorithm uses the grouping characteristics of PD pulses in the 3D plot of the magnitude versus phase versus cycle. This special technique can remove the periodical noise pulses with varying magnitudes, which are very difficult to be removed by other denoising methods. Each of the sub-algorithm has different characteristic and shows different quality of the noise rejection. On that account, a parameter which numerically expresses the noise possessing degree of signal, is defined and evaluated. Using the parameter and above three sub-algorithms, an adaptive complex noise rejection algorithm for the on-line PD diagnosis system is developed. Proposed algorithm shows good performances in the various real PD signals measured from the power apparatuses in the Korean plants.