Partial strain relaxation from the light-emitting diode (LED) with surface-textured p-GaN was observed. The textured device possesses less efficiency droop and a higher current level at the efficiency maximum, as compared with the planar one. The results suggest that surface roughening affects not only the external light extraction but also the internal quantum efficiency. Furthermore, the photoluminescent (PL) measurement at low temperature reveals that the percentage increment of the optical power of the textured LED over that of the planar LED becomes lower. In addition to the effect of frozen nonradiative defect states, the PL difference is related to the strain-correlated quantum-confined Stark effect.