We study thermodynamic responsive properties of a grafted polyanion layer on a planar surface by using statistical density-functional theory. The structure and electrostatics of the grafted layer are explored by varying the strength (epsilon) of dispersion interaction (DPI) and salt concentration (rho(salt)). The brush behaviors are determined by the competition and interplay between the DPI and the screening effect of small ions (counterions and salt ions). The DPI has a positive contribution to brush swelling, while the doping salt has either a positive or negative contribution depending on the concentration. At low surface grafting density (rho(g)), the DPI plays a prominent role at low (rho(salt)); the screening effect dominates the behavior only at high (rho(salt)) At high rho(g), the screening effect is always important because the counterion density inside the brush is high; the electrostatic interaction is weak in most cases so that the brush layer is sensitive to the DPI. Both structure and electrostatics of the grafted layer can be regulated and controlled by varying epsilon and rho(salt). These results provide useful predictions and a fundamental understanding for the thermodynamic properties in a polyelectrolyte-grafted surface.