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The precursors of short and long Gamma Ray Bursts (SGRBs and LGRBs) can serve as probes of their progenitors, as well as shedding light on the physical processes of mergers or core-collapse supernovae. Some models predict the possible existence of Quasi-Periodically Oscillations (QPO) in the precursors of SGRBs. Although many previous studies have performed QPO search in the main emission of SGRBs and LGRBs, so far there was no systematic QPO search in their precursors. In this work, we perform a detailed QPO search in the precursors of SGRBs and LGRBs detected by Fermi/GBM from 2008 to 2019 using the power density spectrum (PDS) in frequency domain and Gaussian processes (GP) in time domain. We do not find any convinced QPO signal with significance above 3 $σ$, possibly due to the low fluxes of precursors. Finally, the PDS continuum properties of both the precursors and main emissions are also studied for the first time, and no significant difference is found in the distributions of the PDS slope for precursors and main emissions in both SGRBs and LGRBs.