The compositions of each part on the focal plane array (FPA) are not likely the same because of the manufacture defects. The defects will cause the inherent differences between pixels while the focal plane array is conducting the photoelectronic conversion. This paper has derived the theoretical model of the nonlinearity of the cooled detector corresponding to the composition x, which is based on the research project of the domestic 640×512 MWIR cooled thermal imager. The infrared radiation received by the FPA and converted into photocurrent, this type of current has significant relationship with the nonlinearity of the detector according to the composition x in the Hg1-xCdxTe material. A black body was used to radiate the detector under the wide working temperature of the detector, and amount of experimental data were collected under every pre-set temperature point. According to the parameter change that influence the photocurrent most, a double exponential fitting model was proposed to describe the nonlinearity characteristics of both the total response and the separate pixel response of the detector. Multiple works were carried out by analyzing the response data in the form of diagram and table to prove the accuracy of the real response fitting by this model.