Phenomena of electron, neutron, atomic and molecular diffraction have been studied in many experiments, and these experiments are explained by many theoretical works. We study neutron single-slit diffraction with a quantum mechanical approach. It is found that the obvious diffraction pattes can be obtained when the singleslit width a is in the range of 3λ～ 60λ. We also find a new quantum effect of the thickness of single-slit which can make a large impact on the diffraction patte. The new quantum effect predicted in our work can be tested by the neutron single-slit diffraction experiment.