The invention provides a method for removing a trace amount of a highly-carcinogenic disinfection byproduct N-nitrosodimethylamine (NDMA) from drinking water by catalytic reduction, which is simultaneously applied to the treatment of NDMA-containing industrial wastewater and contaminated ground water and belongs to the field of water treatment application. Specifically, in the method provided by the invention, commercial nano iron is adopted as a reducing agent, a certain amount of water treatment aluminum sulfate is added into reaction solution, a reaction pH range is controlled to be 4 to 7, and the reaction is performed for 10 to 24 hours under oscillation or stirring to fulfill the aim of removing the trace amount of NDMA from the water. The trace amount of NDMA in the water is treated by the method without controlling the dissolved oxygen of the reaction solution, the removal rate can reach over 80 percent and difficulties in effectively degrading the NDMA by oxidization, absorption and membrane filtration are effectively overcome. Products produced by the reaction mainly comprise ammonia nitrogen, ferrous ions and the like, and can be removed by simple aeration, precipitation or the membrane filtration. The method for treating the drinking water is safe.