Conventionally, evaluation of myocardial T1-times is limited to a single snapshot of the cardiac cycle, leaving much of the dependence between functional and tissue characterization unstudied. Here, we propose an ECG-triggered steady-state Look-Locker technique that allows for functional, cardiac phase-resolved native T1-mapping. Integratedly acquired phase-resolved B1+-maps are used for T1-time correction. High accuracy and good consistency of the T1-times across cardiac phases is shown in phantom scans. In-vivo T1-times show slight underestimation and similar precision compared to saturation-recovery T1-mapping. High visual image quality at all cardiac phases is obtained at temporal resolutions up to 40ms in a single breath-hold.