Balanced steady state free precession (bSSFP) phase-contrast sequences have desirable tissue contrast properties that allow for non-contrast-enhanced cardiovascular flow exams. However, they are susceptible to flow-related signal dephasing especially in regions with highly accelerating flow like the heart. To address this, we propose a variable-density radial view-ordered bSSFP 4D flow sequence. Acquired images show reasonable visualization of cardiac anatomy, and similar velocity measurements in aortic regions. Further sequence modifications are suggested to improve its robustness. If proven to be a viable alternative to the standard exam, bSSFP 4D flow would reduce exam costs and greatly improve patient experience.