Elastic scattering of low-energy electrons from the ground state of hydrogen atoms in dense quantum plasma environments has been studied using an effective range theory. We use the exponential cosine-screened Coulomb potential (ECSCP) to represent the plasma screening effect in a dense quantum plasma. Highly correlated Hylleraas-type wave functions for H(superscript -) are used to determine the effective range of the ion states. The results for S-wave singlet phase shifts in dense quantum plasmas are reported for the incident electron energy in the range for which only the elastic channel is open. Furthermore, we have compared the plasma screening effect of a dense quantum plasma with that of a weakly-coupled plasma, for which the plasma screening effect has been represented by the Debye model. Our results for the unscreened case agree nicely with some of the most accurate results available in the literature.