Binary pulsars are an important target for radio surveys because they present a natural laboratory for a wide range of astrophysics like testing general relativity, including detection of the gravitational waves. The orbital motion of the pulsar which is locked in a binary system causes a frequency shift (a Doppler shift) in their normally very periodic pulse emissions. These shifts cause a reduction in the sensitivity of traditional periodicity searches, caused by the smeared response of the Fourier transform when applied to the Doppler-shifted signal. To correct this smearing Ransom (2001, 2002) developed Fourier domain acceleration search (FDAS) which uses applies matched filtering technique. This method is however limited to a constant acceleration. Andersen and Ransom (2018) broadened the Fourier domain acceleration search to account also for a linear change in the acceleration by implementing Fourier domain "jerk" search into PRESTO software package. This extension increases the number of matched filters used significantly. We have implemented Fourier domain "jerk" search (JERK) on GPUs using CUDA. This work is based on our previous work on FDAS by Dimoudi(2018) and Adamek (2017), where we have used a custom implementation of FFT algorithm which uses shared memory of the NVIDIA GPUs. We have achieved 140x performance increase when compared to the serial implementation of JERK in PRESTO. This work is part of the AstroAccelerate project (Armour et al. 2012), a many-core accelerated time-domain signal processing library for radio astronomy.