Photon counting detectors based on microchannel plate have widespread applications in astronomy. The present paper deeply studies secondary electron of microchannel plate in extreme ultraviolet. A theoretical model describing extreme ultraviolet-excited secondary electron yield is presented, and the factor affecting on the secondary electron yields of both electrode and lead glass which consist of microchannel plate is analyzed according to theoretical formula derived from the model. The result shows that the higher secondary electron yield is obtained under appropriate condition that the thickness of material is more than 20 nm and the grazing incidence angle is larger than the critical angle. Except for several wavelengths, the secondary electron yields of both electrode and lead glass decrease along with the increase in the wavelength. And also the quantum efficiency of microchannel plate is measured using quantum efficiency test set-up with laser-produced plasmas source as an extreme ultraviolet radiation source, and the result of experiment agrees with theoretical analysis.