Theoretical investigation of photonic band gaps or reflection bands in one-dimensional annular photonic crystal (APC) containing double negative (DNG) metamaterials and air has been presented. The proposed structure consists of the alternate layers of dispersive DNG material and air immersed in free space. In order to study photonic band gaps we obtain the reflectance spectrum of the annular PC by employing the transfer matrix method (TMM) in the cylindrical waves for both TE and TM polarizations. In this work we study the effect of azimuthal mode number (m) and starting radius (ρ0) on the three band gaps viz. zero averaged refractive index (zero-nbar) gap, zero permittivity (zero- ε) and zero permeability (zero- μ) gaps. It is found that for m ≥ 1 , zero- μ gap appears in TE mode and zero- ε gap appears in TM mode. The width of both zero- μ and zero- ε gap increases by increasing m values, but the enhancement of zero- μ gap is more appreciable. Also, the effect of ρ0 on the three band gaps (reflection bands) of annular PC structure at the given m-number has been studied, for both TE and TM polarizations. The result shows that in both polarizations zero- ε and zero- μ gaps decreases when ρ0 increases, whereas zero-nbar gap remains invariant.