A universal modulation theory is established to clarify the main parameters affecting the modulation efficiency, making a breakthrough progress on the 1/f noise problem in magnetoresistance (MR) that has not been effectively solved with trial and error for a long time. For achieving a modulation efficiency of 100 %, the theory indicates that the magnetic field strength along the sensitive direction of MR should be designed to be proportional to the displacement of the modulation structure. The established theory is thereafter experimentally demonstrated by proposing a new tunnel magnetoresistance (TMR) accelerometer with the highest modulation efficiency of 87 % than ever. The established theory is not only applicable to various kinds of MR sensors such as magnetometers, displacement meters, accelerometers, resonant galvanometer (Wang galvanometer), as well as other resonant sensors for improving sensing properties, but also a complementary solution to materials research in MR and its relevant field.