In this work, we aimed to derive the $gri$-band period-luminosity (PL) and period-luminosity-color (PLC) relations for late-type contact binaries, for the first time, located in the globular clusters, using the homogeneous light curves collected by the Zwicky Transient Factory (ZTF). We started with 79 contact binaries in 15 globular clusters, and retained 30 contact binaries in 10 globular clusters that have adequate number of data points in the ZTF light curves and unaffected by blending. Magnitudes at mean and maximum light of these contact binaries were determined using a fourth-order Fourier expansion, while extinction corrections were done using the {tt Bayerstar2019} 3D reddening map together with adopting the homogeneous distances to their host globular clusters. After removing early-type and arcsecanomaly arcsec contact binaries, our derived $gri$-band PL and period-Wesenheit (PW) relations exhibit a much larger dispersion with large errors on the fitted coefficients. Nevertheless, the $gr$-band PL and PW relations based on this small sample of contact binaries in globular clusters were consistent with those based on a larger sample of nearby contact binaries. Good agreements of the PL and PW relations suggested both samples of contact binaries in the local Solar neighborhood and in the distant globular clusters can be combined and used to derive and calibrate the PL, PW and PLC relations. The final derived $gr$-band PL, PW and PLC relations were much improved than those based on the limited sample of contact binaries in the globular clusters.