A longer laser resonator length is benefit for laser linewidth, but harmful for single-frequency operation. A novel way is suggested to narrow the bandwidth of a Fabry-Perot (FP) cavity through increasing the derivative of one round-trip phase shift with respect to the frequency. It can be implemented by replacing one of two FP mirrors with a Gires-Tournois etalon (GTE), called FPGT, as a dispersion element. FPGT resonator has additional axial modes due to the GTE reflection phase shift. Theoretical analyses show that the bandwidth of additional axial modes can be 1% of that of a conventional FP cavity. A distributed feedback (DFB) laser diode can employ FPGT resonator to achieve ultra-narrow linewidth laser. It is shown that the effect of refractivity fluctuation in the gain medium on the linewidth is little, and kilohertz linewidth is achievable for such a device.