The extremely rapid reflection of a shock wave from the end wall generated in the shock tube, in addition to the high-frequency content of pressure, inevitably also excites mechanical vibrations. These can potentially produce acceleration-induced spurious signals as part of the dynamic output of the pressure measurement system being calibrated. This paper proposes and evaluates a method for correcting the frequency response of a pressure measurement system obtained with a calibration using a shock tube for the acceleration-induced errors due to vibrations. The proposed method is based on the predetermined frequency response of the pressure measurement system to the accelerations and simultaneous measurements of the vibration accelerations of the pressure sensor during its calibration in the shock tube. The acceleration-induced errors were corrected for a piezoelectric pressure measurement system calibrated in a diaphragmless shock tube developed at the National laboratory for pressure and vacuum at RISE Research Institutes of Sweden, where different vibrational conditions were induced by changing the initial driver pressure, while keeping the initial driven pressure constant. The uncertainty of the correction of the frequency response of the piezoelectric pressure measurement system being calibrated was determined by considering the uncertainty contributions of the measured acceleration frequency response of the pressure measurement system, the measured acceleration of the pressure sensor during its calibration in the shock tube, the generated reference end-wall step pressure and the repeatability of the correction. The results show that the proposed method effectively eliminates acceleration-induced errors in the sensitivity and phase frequency responses of an acceleration-sensitive piezoelectric pressure measurement system being calibrated with a shock tube.