A new and distinct Gypsophila plant named `DANGYP39 ` characterized by having globular-shaped, double flowers, 9 to 11 mm in diameter; conic, pink flowers arranged in clusters, creating a wide and impressive conic structure; 7-9 stems per plant in first flash, medium flash duration; erect, stable growth habit, branching from lower part of main stem, 85 to 95 cm in height; uniformly good quality of inflorescence year round; good post-production longevity, with vase life of 10 to 14 days; and commercially suitable product; marketed as a cut flower.