Convection enhanced delivery is promising to overcome the blood brain barrier. However, the treatment is less efficient in clinic due to the rapid elimination of small molecular drugs in brain tumours. In this study, numerical simulation is applied to investigate the convection enhanced delivery of liposome encapsulated doxorubicin under various conditions, based on a 3-D brain tumour model that is reconstructed from magnetic resonance images. Treatment efficacy is evaluated in terms of the tumour volume where the free doxorubicin concentration is above LD90. Simulation results denote that intracerebral infusion is effective in increasing the interstitial fluid velocity and inhibiting the fluid leakage from blood around the infusion site. Comparisons with direct doxorubicin infusion demonstrate the advantages of liposomes in enhancing the doxorubicin accumulation and penetration in the brain tumour. Delivery outcomes are determined by both the intratumoural environment and properties of therapeutic agents. The treatment efficacy can be improved by either increasing the liposome solution concentration and infusion rate, administrating liposomes in the tumour with normalised microvasculature density, or using liposomes with low vascular permeability. The delivery is less sensitive to liposome diffusivity in the examined range (E-11~E-7 cm2/s) as convective transport is dominative in determining the liposome migration. Drug release rate is able to be optimised by keeping a trade-off between enhancing the drug penetration and providing sufficient free doxorubicin for effective cell killing. Results from this study can be used to improve the regimen of CED treatments.