A free-running multi-echo GRE approach was proposed for whole-heart fat quantification. Retrospective extraction of cardiac and respiratory motion states was achieved using integrated Pilot Tone navigation, enabling a free-breathing non-ECG-triggered acquisition. Following a motion-resolved compressed sensing based image reconstruction of the separate echoes, fat fraction, water fraction, R2* and B0 maps, as well as separated fat and water images, were calculated. Free-running acquisition parameters were optimized in a fat phantom. Volunteer experiments demonstrated the feasibility of motion-resolved free-running fat-fraction mapping technique in a 6-minute scan time.