Disclosed herein is a prompt gamma-ray detection apparatus for analyzing chemical materials using femtosecond pulse laser-induced neutrons, which can be effectively used in the nondestructive inspection of various materials, such as metals, coal, cement, radioactive materials and the like as well as explosives and chemical materials, and which can provide better measurement results for the analysis of basic materials, and a method of measuring prompt gamma-rays using the apparatus. The prompt gamma-ray detection apparatus is advantageous because it can non-destructively analyze the elements in a chemical sample using a femtosecond pulse laser-induced neutron generator that solves the problems of an atomic reactor for research or a radioactive isotope as a neutron radiation source.