The serious separation of electron–hole wavefunctions, which is caused by the built-in electric field, prevents electron–hole radiative recombination in quantum wells (QWs) in high-In-content InGaN-based red light-emitting diodes (LEDs). Here, we propose a staggered structure that inserts an ultrathin InN layer in the single quantum well (SQW) to reduce the piezoelectric polarization and suppress the quantum confined Stark effect (QCSE). We have numerically simulated the effects of SQW with the InN insertion layer (IL) on the energy band structure and electron–hole wavefunctions of the red LED. Owing to alleviated piezoelectric polarization and improved overlaps of electron–hole wavefunctions, the simulation results have revealed that the internal quantum well (IQE) of the red LED with InN IL exhibits 42% higher than that of the red LED with a square-shaped QW (SSQW) at 60 A/cm2, and the efficiency droop ratio of red LED with InN IL is 48% lower than that of red LEDs with SSQW. Furthermore, we have found that the position of InN IL can affect the energy states of carriers, which has a great influence on the IQE and peak emission wavelength of red LEDs.