Blue InGaN/GaN light-emitting diodes with undoped, heavily Si-doped, Si delta-doped, heavily Mg-doped, Mg delta-doped, and Mg-Si pin-doped GaN barrier are investigated numerically. The simulation results demonstrate that the Mg-Si pin-doping in the GaN barrier effectively reduces the polarization-induced electric field between the InGaN well and the GaN barrier in the multiple quantum well, suppresses the quantum-confined Stark effect, and enhances the hole injection and electron confinement in the active region. For this light-emitting diode (LED) device structure, we found that the turn-on voltage is 2.8 V, peak light emission is at 415.3 nm, and internal quantum efficiency is 85.9% at 100 A cm^-2. It is established that the LED device with Mg-Si pin-doping in the GaN barrier has significantly improved efficiency and optical output power performance, and lower efficiency droop up to 400 A cm^-2 compared with LED device structures with undoped or Si(Mg)-doped GaN barrier.