We report a search for the rare charmless decay $B^+rightarrowoverline{K}{}^{*0}K^{*+}$ using a data sample of $772times10^6$ $Bbar{B}$ pairs collected at the $Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. No statistically significant signal is found and a 90% confidence-level upper limit is set on the decay branching fraction as $ mathcal{B}(B^+rightarrowoverline{K}{}^{*0}K^{*+}) <1.31times 10^{-6}$.