We proposed and fabricated a microwave-frequency photonic fiber grating (MPFG) by femtosecond laser micromachining on optical fibers. Illuminated by low coherent light source, the MPFG can be interrogated using proposed microwave photonic system to show the resonant peaks in microwave frequency domain. We studied the working principle and characteristics of this device. After that, we discussed the influence of fiber type, apodization and light source coherence lengths on this device. The device can also respond to ambient temperature change like fiber optic sensors.