The effectiveness of anticancer treatments is often hampered by the serious side effects owing to toxicity of anticancer drugs and their undesirable uptake by healthy cells in vivo. Thermosensitive liposome-mediated drug delivery has been developed as part of research efforts aimed at improving therapeutic efficacy while reducing the associated side effect. Since multiple steps are involved in the transport of drug-loaded liposomes, drug release, and its uptake, mathematical models become an indispensible tool to analyse the transport processes and predict the outcome of anticancer treatment. In this study, a computational model is developed which incorporates the key physical and biochemical processes involved in drug delivery and cellular uptake. The model has been applied to idealized tumour geometry, and comparisons are made between continuous infusion of doxorubicin and thermosensitive liposome-mediated delivery. Results show that thermosensitive liposome-mediated delivery performs better in reducing drug concentration in normal tissues, which may help lower the risk of associated side effects. Compared with direct infusion over a 2-hour period, thermosensitive liposome delivery leads to a much higher peak intracellular concentration of doxorubicin, which may increase cell killing in tumour thereby enhancing the therapeutic effect of the drug.