The present invention relates to a method for leaching precious metals contained in a waste denitrification catalyst by using a pressure leaching process, and more specifically, to a method for leaching precious metals contained in a waste denitrification catalyst by using a pressure leaching process, the method comprising the steps of: forming a mixture by mixing a waste denitrification catalyst with a sodium salt solution; and leaching vanadium and tungsten contained in the mixture by feeding the mixture into a sealed pressurized reactor, and then heating and stirring the mixture.