Biopolymers bearing hydrophobic side-chains, such as hydrophobically modified chitosan (hmC), can connect liposomes into a gel network via hydrophobic interactions. In this paper, we show that such liposome gels possess an attractive combination of properties for certain drug delivery applications. Their shear-thinning property allows these gels to be injected at a particular site, while their gel-like nature at rest ensures that the material will remain localized at that site. Moreover, drugs can be encapsulated in the interior of the liposomes and delivered at the local site for an extended period of time. The presence of two transport resistances - from the liposomal bilayer and the gel network is shown to be responsible for the sustained release; in turn, disruption of the liposomes both weakens the gel and causes a faster release. We have monitored release kinetics from liposome gels of a cationic anticancer drug doxorubicin (Dox) encapsulated in liposomes. Sustained release of Dox from these gels and the concomitant cytotoxic effect could be observed for over a week.