Coupling characteristics between a single mode fiber (SMF) and a waveguide embedded in a glass chip via a graded index fiber (GIF) tip are investigated at a wavelength of 976 nm. The GIF tips comprise a coreless fiber section and a GIF section. A depressed cladding waveguide in a ZBLAN glass chip with a core diameter of 35 μm is coupled with GIF tips that have a range of coreless fiber and GIF lengths. An experimental coupling efficiency as high as 88% is obtained while a numerical simulation predicts 92.9% for the same GIF tip configuration. Since it is measured in the presence of Fresnel reflection, it can be further improved by anti-reflection coating. Additionally, it is demonstrated that a gap can be introduced between the chip waveguide and the GIF tip while maintaining the high coupling efficiency, thus allowing a thin planar optical component to be inserted. The results presented here will enable miniaturization and simplification of photonic chips with integrated waveguides by replacing bulk coupling lenses with integrated optical fibers.