  The LHCb Collaboration recently gave an update on testing lepton flavour
universality with $B^+ \rightarrow K^+ \ell^+ \ell^-$, in which a 3.1 standard
deviations from the standard model prediction was observed. The g-2 experiment
also reports a 3.3 standard deviations from the standard model on muon
anomalous magnetic moment measurement. These deviations could be explained by
introducing new particles including leptoquarks. In this paper, we show the
possibility to search for heavy spin-1 leptoquarks at a future TeV scale muon
collider by performing studies from three channels: 1) same flavour final
states with either two bottom or two light quarks, 2) different flavour quark
final states, and 3) a so-called "VXS" process representing the scattering
between a vector boson and a leptoquark to probe the coupling between
leptoquark and tau lepton. We conclude that a 3 TeV muon collider with
$3~{ab^{-1}}$ of integrated luminosity is already sufficient to cover the
leptoquark parameter space in order to explain the LHCb lepton flavour
universality anomaly.
