A liposomal composition and a method of using the same for achieving intracellular delivery of a liposome-entrapped agent is described. The liposomes are composed of a pH sensitive lipid and include a targeting ligand to direct the liposomes to a target cell. The liposomes also include a stabilizing component, such a polymer-derivatized lipid, where the polymer is attached to the lipid by a releasable linkage. Administration of the liposomes results in cellular internalization and destabilization of the liposome for intracellular delivery of the entrapped agent.