A tunable filter is formed when a plasma defect is introduced in the one-dimensional dielectric-air microwave photonic crystal. Plasma is a dispersive medium and its equivalent refractive index is related to the frequency of the incident electromagnatic wave and the plasma frequency， so it is feasible to shift the syntonic frequency of plasma defect by changing the plasma parameters, which behaves as a tunable filter. In the numerical simulation， the finite-difference time-domain method and the piecewise linear current density recursive convolution finite-difference time-domain method are applied to the dielectric and plasma， respectively. The results show that the filter channel of this microwave photonic crystal can be tuned in a wide band in the photonic band-gap by changing the plasma frequency.