Cubosomes consist in submicron size particles of lipid bicontinuous cubic phases stabilized by surfactant polymers. They provide an appealing road towards the practical use of lipid cubic phases for pharmaceutical and cosmetic applications, and efforts are currently being made to control the encapsulation and release properties of these colloidal objects. We overcome in this work the lack of sensitivity of monoolein cubosomes to pH conditions by using a pH sensitive polymer designed to strongly interact with the lipid structure at low pH. Our cryo-transmission electron microscope (cryo-TEM) and small-angle X-ray scattering (SAXS) results show that in the presence of the polymer the cubic phase structure is preserved at neutral pH, albeit with a larger cell size. At pH 5.5, in the presence of the polymer, the nanostructure of the cubosome particles is significantly altered, providing a pathway to design pH-responsive cubosomes for applications in drug delivery.