Abstract: The present invention relates to a Cucumis melo seed designated 34-780 RZ, which may exhibit andromonoecious sex expression, a circular to slightly broad elliptic shape in longitudinal section, a very light to light intensity of the grey ground color of the fruit skin, a small to medium size of the pistil scar, a medium thickness of the cork layer with a linear and netted pattern of a medium density, medium time of ripening, a long to very long shelf life, and intermediate resistance to powdery mildew Podosphaera xanthii (Px) race 1, race 2, race 5. The present invention also relates to a Cucumis melo plant produced by growing the 34-780 RZ seed. The invention further relates to methods for producing the melon cultivar, represented by melon variety 34-780 RZ.