Shearography is a non-contact, full-field, and high-precision optical deformation measurement technology. There is a lot of random noise in the acquired speckle fringe pattern caused by environmental factors, which affects the measurement accuracy. The traditional denoising methods easily cause the fringe information to be lost or even damaged while filtering out the noise. To solve this problem, we propose an image denoising method by combining sine and cosine transform and bitonic filtering. In this method, the phase fringe image is firstly obtained by sine and cosine transform. Secondly, the two images are denoised by the bitonic filtering method respectively. Finally, the filtered two images are merged into the final phase fringe image. Experimental results show that for the filtered phase pattern, the speckle suppression index is 0.999 and the average retention index is 2.995, which prove that the proposed method can improve the quality of the phase pattern better than the traditional denoising method, and can preserve the details and edge information of the phase fringes to a large extent.