This article describes the design and synthesis of a new series of hydrogel membranes composed of trialkyne derivatives of glycerol ethoxylate and bisphenol A diazide (BA-diazide) or diazide-terminated PEG600 monomer via a Cu(I)-catalyzed photoclick reaction. The water-swollen hydrogel membranes display thermoresponsive actuation and their lower critical solution temperature (LCST) values are determined by differential scanning calorimetry. Glycerol ethoxylate moiety serves as the thermoresponsive component and hydrophilic part, while the azide-based component acts as the hydrophobic comonomer and most likely provides a critical hydrophobic/hydrophilic balance contributing also to the significant mechanical strength of the membranes. These hydrogels exhibit a reversible shape-memory effect in response to temperature through a defined phase transition. The swelling and deswelling behavior of the membranes are systematically examined. Due to the click nature of the reaction, easy availability of azide and alkyne functional-monomers, and the polymer architecture, the glass transition temperature (T-g) is easily controlled through monomer design and crosslink density by varying the feed ratio of different monomers. The mechanical properties of the membranes are studied by universal tensile testing measurements. Moreover, the hydrogels show the ability to absorb a dye and release it in a controlled manner by applying heat below and above the LCST.