Creating artificial cells with a dynamic cytoskeleton, akin to those in living cells, is a major goal in bottom-up synthetic biology. In this study, we demonstrate the in situ polymerization of microtubules encapsulated in giant polymer-lipid hybrid vesicles (GHVs) composed of 1,2-dioleoyl-sn-glycero-3-phosphocholine and an amphiphilic block copolymer. The block copolymer is comprised of poly(cholesteryl methacrylate-co-butyl methacrylate) as the hydrophobic block and either poly(6-O-methacryloyl-D-galactopyranose) or poly(carboxyethyl acrylate) as the hydrophilic extension. Depending on the concentrations of guanosine triphosphate (GTP) or its slowly hydrolyzable analog, guanosine-5'-[(α,β)-methyleno]triphosphate (GMPCPP), different microtubule morphologies are observed, including encapsulated microtubule networks, spike protrusions, as well as membrane-associated or aggregated microtubules. Overall, this work represents a step forward in mimicking the cellular cytoskeletons and uncovering the influence of membrane composition on microtubule morphologies.