An on-chip optical filter having Fabri-Perot resonators and a spectrometer may include a first sub-wavelength grating (SWG) reflecting layer and a second SWG reflecting layer facing each other. A plurality of Fabri-Perot resonators are formed by the first SWG reflecting layer and the second SWG reflecting layer facing each other. Each of the Fabri-Perot resonators may transmit light corresponding to a resonance wavelength of the Fabri-Perot resonator. The resonance wavelengths of the Fabri-Perot resonators may be determined according to duty cycles of grating patterns.