The pixel-wise nonlinear regression method for T1-mapping is susceptible to noise. We propose a convolutional neural network framework for fast and robust cardiac MRI T1-mapping. A dense type of architecture is used for producing denoised T1-maps. Results show the proposed framework improves PSNR by 6dB compared to the pixel-wise nonlinear regression. The Wilcoxon signed rank test shows a significant reduction in the standard deviation of T1-values produced by the proposed method as compared to nonlinear regression. After training, the time required for producing one T1-map from the undersampled images is 6.45 seconds.