Using a material with a low elastic modulus and a high dielectric constant as the dielectric layer of a capacitive pressure sensor is an ideal method to improve the sensitivity of the sensor and the initial capacitance signal. However， two properties of these materials often conflict with each other. To address this problem， a liquid metal elastomer foam is proposed， which has a low elastic modulus （10.2 kPa）， strong compressibility （70% strain） and high dielectric constant （5.5~20.9）. Using the foam as the dielectric layer and designing a flexible electrode with a shielding layer， a flexible capacitive pressure sensor with high sensitivity and large initial capacitance signal is developed. The test results show that the sensitivity of the sensor is as high as 0.36 kPa-1， the response/recovery speed is fast （<49 ms）， and the hysteresis is low （8.7%）. At the same time， it can detect tiny pressures as low as 4.9 Pa， and has good stability and reliability. In addition， the effectiveness of the developed sensor is verified through the test of the bending deflection of the sieve plate of the relaxation screen. Compared with the measured value of the laser displacement sensor， experimental results show that the flexible pressure sensor can accurately detect the change of the bending deflection of the sieve plate of the relaxation sieve