  Variability is a typical observation feature of Fermi blazars, sometimes it
shows quasi-periodic oscillation (QPO). In this work, we obtained 5-day binned
light curves (with a time coverage of $\sim$ 12.9 yr) for S5 1044+71 based on
Fermi LAT data, adopted five different methods: Date-compensated Discrete
Fourier Transform (DCDFT), Jurkevich (JV), Lomb-Scargle Periodogram (LSP), a
Fortran 90 program (REDFIT) and the Weighted Wavelet Z-transform (WWZ) to the
$\gamma$-ray light curve, and found a possible QPO of 3.06 $\pm$ 0.43 yr at the
significance level of $\sim3.6\sigma$. A binary black hole model including
accretion model and dual-jets model is used to explain this quasi-periodic
variability. We also estimated the Doppler factors and the apparent velocity
for the two jet components. We speculate that this $\gamma$-ray quasi-periodic
modulation suggest the presence of a binary supermassive black hole in S5
1044+71.
