Native myocardial T1 mapping provides information for the detection of diffuse fibrosis in different cardiac diseases. Here we present simultaneous T1 mapping and cine imaging with a resolution of 1.3x1.3mm² using model-based iterative reconstruction. T1 times in the septum were 1285±46ms compared to 1240±28ms obtained with MOLLI. In contrast to MOLLI, the proposed approach did not show any heart rate dependence of T1. In addition, the approach allows T1 mapping of challenging structures, such as the right ventricle and the apex. Functional assessment of reconstructed cine images did not show any significant differences compared to a standard Cartesian cine scan.