The invention discloses a leading trailing shoe drum brake applying force through trailing shoe giant magnetostictive and a method of the leading trailing shoe drum brake. The leading trailing shoe drum brake comprises a left brake shoe, a left brake piece, a brake wheel cylinder, a brake drum, a right brake piece, a right brake shoe, a reset spring, a right connection piece, a right limiting cover, a right coil fixing cover, an assistor shell, an assistor base, a left coil fixing cover, a left limiting cover, a left connection piece, a left elastic rubber gasket, a left adjusting spacer, a left wire outlet hole, a giant magnetostictive column, an exciting coil, a coil framework, a right wire outlet hole, a right adjusting spacer and a right elastic rubber gasket. According to the leading trailing shoe drum brake applying force through trailing shoe giant magnetostictive and the method of the leading trailing shoe drum brake, to solve the problem that a trailing shoe in a leading trailing shoe brake is low in braking efficiency, the giant magnetostictive column is utilized to conduct braking and force applying on the trailing shoe, so that the overall braking efficiency of the leading trailing shoe drum brake is improved, the braking distance is reduced, and vehicle running safety is improved; besides, the leading trailing shoe drum brake further has the advantages that the drum brake is good in reliability, convenient to use and free of affecting working of an original braking system after reformation is conducted, and a parking braking mechanism is arranged conveniently.