An atom interferometer based on Doppler-insensitive Raman transition is proposed, which has sharply peaked interference fringes for multi-wave interference. We show that two sets of counter-propagating Doppler-insensitive Raman beam pairs can be used to construct a new type of multi-wave beam splitter, which can be used to construct an atom interferometer. Although the spacing between adjacent diffraction orders of the interferometer is small, they can be distinguished by the internal state of the atom. Our analysis shows that the width of the fringes of this atom interferometer is inversely proportional to the width (duration) of the beam splitter and the Rabi frequency of the Raman beams, that is, the interferometer can achieve high resolution at high light intensity and long pulse width.