Respiratory motion-induced image blurring and artifacts can compromise image quality in dynamic contrast-enhanced MRI (DCE-MRI) of the liver. Despite remarkable advances in respiratory motion detection and compensation in past years, these techniques have not yet seen widespread clinical adoption. The accuracy of image-based motion detection can be especially compromised in the presence of contrast enhancement and/or in situations involving deep and/or irregular breathing patterns. This work proposes a framework that combines GRASP-Pro (Golden-angle RAdial Sparse Parallel MRI with imProved performance) MRI with a new radial sampling scheme called navi-stack-of-stars for free-breathing DCE-MRI of the liver without the need for explicit respiratory motion compensation. A prototype 3D golden-angle radial sequence with a navi-stack-of-stars sampling scheme that intermittently acquires a 2D navigator was implemented. Free-breathing DCE-MRI of the liver was conducted in 24 subjects at 3T including 17 volunteers and 7 patients. GRASP-Pro reconstruction was performed with a temporal resolution of 0.34-0.45 s per volume, whereas standard GRASP reconstruction was performed with a temporal resolution of 15 s per volume. Motion compensation was not performed in all image reconstruction tasks. Liver images in different contrast phases from both GRASP and GRASP-Pro reconstructions were visually scored by two experienced abdominal radiologists for comparison. The nonparametric paired two-tailed Wilcoxon signed-rank test was used to compare image quality scores, and the Cohen's kappa coefficient was calculated to evaluate the inter-reader agreement. GRASP-Pro MRI with sub-second temporal resolution consistently received significantly higher image quality scores (P < 0.05) than standard GRASP MRI throughout all contrast enhancement phases and across all assessment categories. There was a substantial inter-reader agreement for all assessment categories (ranging from 0.67 to 0.89). The proposed technique using GRASP-Pro reconstruction with navi-stack-of-stars sampling holds great promise for free-breathing DCE-MRI of the liver without respiratory motion compensation.