Within the effective-mass approximation, the influences of hydrostatic pressure on the exciton binding energies, emission wavelengths and electron-hole recombination rates for a heavy-hole exciton in strained wurtzite (WZ) GaN/Al0.15Ga0.85N cylindrical quantum dot (QD) with finite potential barriers are investigated via a variational procedure, with considering the strong built-in electric field (BEF) effect and strain dependence of material parameters. Numerical results show that the exciton binding energies and electron-hole recombination rates both increase almost linearly, and the emission wavelengths are monotonically reduced with the increase of the applied hydrostatic pressure. The hydrostatic pressure has a remarkable influence on the exciton binding energy and electron-hole recombination rate for the QD with a small size. Furthermore, the height of GaN QDs must be less than 5.5 nm for an efficient electron-hole recombination process due to strain effects.