We explore, theoretically and experimentally, the spatial (angular) filtering of two-dimensional light beams by longitudinally chirped axisymmetric photonic microstructures. The structures comprise a set of planes of concentric rings with the separation between the plates smoothly varying along the propagation direction. Axisymmetric structures were recorded in a bulk of glass, in which the refractive index has been modulated using tightly focused femtosecond laser pulses. We show that the spatial filtering recently shown in nonchirped axisymmetric structures can be substantially improved by the chirp: the angular range of filtering was increased approximately two times. The numerical study reveals that the filtering efficiency can be strongly increased using the longer and larger index contrast axisymmetric photonic structures.