The performance of perovskite light-emitting diodes (PeLEDs) has progressed rapidly in recent years, with electroluminescence efficiency now reaching 20%1–12. However, devices, so far, have featured small areas and usually show notable variation in device-to-device performance. Here, we show that the origin of suboptimal device performance stems from inadequate hole injection, and that the use of a hole-transporting polymer with a shallower ionization potential can improve device charge balance, efficiency and reproducibility. Using an ITO/ZnO/PEIE/FAPbI3/poly-TPD/MoO3/Al device structure, we report a 799 nm near-infrared PeLED that operates with an external quantum efficiency (EQE) of 20.2%, at a current density of 57 mA cm−2 and a radiance of 57 W sr−1 m−2. The standard deviation in the device EQE is only 1.2%, demonstrating high reproducibility. Large-area devices measuring 900 mm2 operate with a high EQE of 12.1%, and are shown to suit medical applications such as subcutaneous deep-tissue illumination and heart rate monitoring. Near-infrared LEDs as large as 30 × 30 mm2 in size are fabricated on both rigid and flexible substrates.