A motion correction method for myocardial T1 mapping using Self-supervised Deep learning based Registration with contrAst seParation (SDRAP) was proposed. A sparse coding based method was firstly proposed to separate the contrast component from T1w images. Then, a self-supervised deep neural network was developed to register contrast separated images, followed by the signal fitting to generate motion corrected T1 maps. Models were trained and tested in 47 healthy volunteers using MOLLI sequence, and compared with Free Form Deformation method. Results showed the proposed method can achieve better performance in registration and T1 mapping with higher efficiency (7x acceleration).