Soft pressure sensors are one class of the essential devices for robotics and wearable device applications. Despite the tremendous progress, sensors that can reliably detect both positive and negative pressures have not yet been demonstrated. In this paper, we report a soft capacitive pressure sensor made using a convenient and low-cost screen-printing process that can reliably detect both positive and negative pressures from −60 kPa to 20 kPa. The sensor is made with an Ecoflex-0030 dielectric layer, conductive and stretchable poly(3,4-ethylenedioxythiophene): poly(styrenesulfonate) (PEDOT:PSS) (with ionic additives) electrodes and polydimethylsiloxane (PDMS) encapsulation layers. Air gaps are designed and incorporated into the dielectric layer to significantly enhance the sample deformation and pressure response especially to negative pressure. The sensor exhibits repeatable response for thousands of cycles, even under bending or stretching conditions. Lastly, to demonstrate the practical application, a 12×12-pixel sensor array that can automatically measure both positive and negative pressure distributions has been reported under −20 kPa and 10 kPa.