In consideration of the lower imaging Signal to Noise Ratio(SNR) and serious mixed noise of a micro-focus X-ray inspector, a denoising method was proposed for the images corrupted with mixed multiplicative noise and additive noise. Firstly, an image model was established to represent the micro-focus X-ray images with mixed multiplicative and additive noises. Then, to remove the mixed noises, the objective functions were proposed based on the principle of total variation and sparse representation. Finally, the multiplicative noise and the additive noise were removed by explicit difference method and gradient projection in steps. Experiment results show that the proposed method enhances the Mean to Standard deviation Ratio(MSR) of the images by 10.9% in smooth areas, the Laplacian Sum(LS) by 15.6% in detail areas as compared with total variation algorithm for the additive noise model. The experiments demonstrate that the proposed method not only removes the mixed noises in X-ray image but also retains the details of the image edge. It meets the requirements of integrated circuit detection for image smoothness and detail definition.