For the reconstruction of pixel-wise T1 maps, 3-parameter fit model is highly accurate, but is sensitive to noise. Therefore, it is desirable to develop a robust method to reduce sensitivity to noise when 3-parameter fit model is used. In this work, we propose a robust denoising method based on tissue characteristics to improve precision of myocardial T1 mapping. In phantom and in-vivo studies, denoising filtering provided similar T1 measurements with significantly improved precision. This technique will make 3-parameter fit model more favorable by reducing sensitivity to noise and will allow for more accurate and precise myocardial T1 mapping.