Most of the computational models of drug transport in vascular tumours assume a uniform distribution of blood vessels through which anti-cancer drugs are delivered. However, it is well known that solid tumours are characterized by dilated microvasculature with non-uniform diameters and irregular branching patterns. In this study, the effect of heterogeneous vasculature on drug transport and uptake is investigated by means of mathematical modelling of the key physical and biochemical processes in drug delivery. An anatomically realistic tumour model accounting for heterogeneous distribution of blood vessels is reconstructed based on magnetic resonance images of a liver tumour. Numerical simulations are performed for different drug delivery modes, including direct continuous infusion and thermosensitive liposome-mediated delivery, and the anti-cancer effectiveness is evaluated through changes in tumour cell density based on predicted intracellular concentrations. Comparisons are made between regions of different vascular density, and between the two drug delivery modes. Our numerical results show that both extra- and intra-cellular concentrations in the liver tumour are non-uniform owing to the heterogeneous distribution of tumour vasculature. Drugs accumulate faster in well-vascularized regions, where they are also cleared out more quickly, resulting in less effective tumour cell killing in these regions. Compared with direct continuous infusion, the influence of heterogeneous vasculature on anti-cancer effectiveness is more pronounced for thermosensitive liposome-mediated delivery.