The prospects for measuring the branching fraction of $H to mu ^+ mu ^-$ at the International Linear Collider (ILC) have been evaluated based on a full detector simulation of the International Large Detector (ILD) concept, considering centre-of-mass energies ($sqrt{s}$) of 250 GeV and 500 GeV. For both $sqrt{s}$ cases, the two final states $e^+ e^- to qoverline{q}H$ and $e^+ e^- to u overline{ u}H$ have been analyzed. For integrated luminosities of 2 ab$^{-1}$ at $sqrt{s} = 250$ GeV and 4 ab$^{-1}$ at $sqrt{s} = 500$ GeV, the combined precision on the branching fraction of $H to mu ^+ mu ^-$ is estimated to be 17{%}. The impact of the transverse momentum resolution for this analysis is also studied.
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