A linear frequency domain grating and a multiband spectrometer having the same. The linear frequency domain grating includes a dispersive optical element and a diffractive optical element being substantially in contact with the dispersive optical element or being substantially integrated with the dispersive optical element, configured to receive a beam of incident light along an incident optical path, and diffract and disperse it into its constituent spectrum of frequencies of the light that is output from the dispersive optical element along an output optical path, such that the output light has a spatial distribution on a focal plane in the output optical path that is a linear function of the frequency. The linear frequency domain grating is a transmissive-type grating or a reflective-type grating, depending on whether the incident optical path and the output optical path are in different sides or the same side of the diffractive optical element.