MRI-controlled tumor treatment by High Intensity Focused Ultrasound (HIFU) is challenging in the abdominal organs because of the breathing motion. We experimentally demonstrated a self-scanning method for motion compensation by passively scanning the tissue passing through the static focal point. Ex vivo turkey samples were subjected to a breathing-like non-periodic motion and the HIFU power was modulated using the velocity information from landmark tracking on simultaneous ultrasound images. MR imaging provided targeting and on-line thermometry. Temperature map were computed using the reference-less PRFS method. A dramatic improvement of the isotherms uniformity score was achieved for rectilinear volumetric ablation.