An improved precision rectifier circuit based on the analog multiplexer was described.Different from the traditional methods,this circuit reduces the nonlinearity without using diodes or matched resistors.And a capacitive micro-displacement sensor was designed based on this improved circuit.The analysis on the experimental results shows that the linearity of this sensor is better than 0.6‰ within the measure range of 0~1.6 mm.And the sensitivity is 4.3 V/mm.