This paper reports the first demonstration of beta-phase gallium oxide as optical waveguides on sapphire substrates grown by metal-organic chemical vapor deposition (MOCVD). The propagation losses from visible to ultraviolet spectra were comprehensively studied. By optimizing the fabrication processes, minimum propagation loss was identified to be 3.7 dB/cm at the wavelength of 810 nm, which is comparable to other wide bandgap materials within the III-N family (GaN, AlN). To further reveal the underlying loss mechanisms, several physical mechanisms such as two-photon absorption, sidewall scattering, top surface scattering, and bulk scattering were taken into consideration. The results obtained from this work suggest that beta-Ga2O3 is promising for ultraviolet-visible spectrum integrated photonic applications.