We present a four-flavour lattice calculation of the leading-order hadronic vacuum polarisation contribution to the anomalous magnetic moment of the muon, a?hvp, arising from quark-connected Feynman graphs. It is based on ensembles featuring Nf=2+1+1 dynamical twisted mass fermions generated by the European Twisted Mass Collaboration (ETMC). Several light quark masses are used in order to yield a controlled extrapolation to the physical pion mass. We employ three lattice spacings to examine lattice artefacts and several different volumes to check for finite-size effects. Including the complete first two generations of quarks allows for a direct comparison with phenomenological determinations of a?hvp. Our final result involving an estimate of the systematic uncertainty a?hvp=6.74 (21)(18) 10-8 shows a good overall agreement with these computations.