Measurement of partial discharge (PD) paves a way for transformer insulation diagnosis. However, noise always interferes with PD signals and can jeopardize the diagnostic reliability. Therefore, it is necessary to adopt signal processing techniques to remove noise from collected signals. Among various types of noise, stochastic noise is considerably difficult to remove due to its similarity with PD signals. This paper proposes an effective method, which adopts fractal dimension and entropy analyses to remove stochastic noise. To verify the proposed method, PD measurements have been performed on a number of experimental models and a substation transformer. Results prove that PD signals can be extracted while the noise can be eliminated from collected noise-corrupted signals by using the proposed method. A comparison with a wavelet transform-based noise removal method has also been made in the paper.