We analized the double production and the triple self-coupling of the standard model Higgs boson at future $\gamma \gamma$ collider energies, with the reactions $\gamma\gamma \rightarrow f \bar f HH$ $(f=b, t)$. We evaluated the total cross section for $f\bar fHH$ and calculated the total number of events considering the complete set of Feynman diagrams at tree-level. We varied the triple coupling $\kappa\lambda_{HHH}$ within the range $\kappa=-2$ and +2. The numerical computation was done for the energy which is expected to be available at a possible Future Linear $\gamma\gamma$ Collider with a center-of-mass energy $500-3000$ $GeV$ and luminosities of 1000 and 5000 $fb^{-1}$. We found that the number of events for the process $\gamma\gamma \rightarrow t \bar t HH$, taking into account the decay products of both $t$ and $H$, is enough to obtain an accurate determination of the triple Higgs boson self-coupling.