We have made an investigation to study the plasma screening effect of dense quantum plasmas on the photodetachment cross section of hydrogen negative ion within the framework of dipole approximation. Plasma screening effect has been taken care of by the exponential cosine-screened Coulomb potential (ECSCP). The asymptotic forms of highly correlated wave functions for the initial bound states of H(-) and the plane wave form for the final e(-)-H states are used to evaluate the transition matrix elements. Results for photodetachment cross section in dense quantum plasmas are reported for the plasma screening parameter in the range [0.0,0.6] (in a(0)(-1)). In respect of the photodetachment process of H(-), we have also compared the plasma screening effect of a dense quantum plasma with that of a weakly coupled plasma for which 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.