In this work we report on a new method for the cationic polymerization of glycidol by citric acid at ambient and solvent free conditions. In this polymerization, citric acid is a proton donor and is able to incorporate in the structure of polyglycerol by reaction with the activated monomer. The molecular weight and degree of branching of the synthesized polymers are affected by the glycidol/citric acid molar ratios and reaction temperature. Due to the citric acid core of the hyperbranched polyglycerols, they are able to break down into the smaller segments at neutral or acidic conditions. Apart from citric acid, glycidol, and water, other reagents or organic solvents have not been used in the synthetic and purification processes. Taking advantage of the green synthesis and ability to cleave under physiological conditions, in addition to the intrinsic biocompatibility of polyglycerol, the synthesized polymers are promising candidates for future biomedical applications.