A simple photonic approach to generate an ultra-narrow linewidth microwave signal is proposed and experimentally demonstrated. In this scheme, a multi-wavelength Brillouin fiber laser (BFL) with a double-loop and un-pumped polarization maintaining erbium doped fiber (PM-EDF) is used. The double-loop configuration includes a 50 m long single-mode fiber (SMF) and a 10 m long SMF as Brillouin gain. The threshold and linewidth of the microwave source can be improved by using a double loop, while a 4 m long un-pumped PM-EDF is used to suppress unwanted side-modes. A dual-wavelength optical signal is heterodyned at the high-speed photo detector to produce a microwave signal by adjusting the polarization controller and the wavelength of the Brillouin pump. As a result, a tunable microwave signal from 10.605 to 10.887 GHz can be obtained. The linewidth of the microwave signal is about 14.4 kHz, and the side-mode suppression ratio is about 30 dB.