Polarization-insensitive semiconductor optical amplifiers (SOAs) in all-optical networks can improve the signal-light quality and transmission rate. Herein, to reduce the gain sensitivity to polarization, a multi-quantum-well SOA in the 1550 nm band is designed, simulated, and developed. The active region mainly comprises the quaternary compound InGaAlAs, as differences in the potential barriers and wells of the components cause lattice mismatch. Consequently, a strained quantum well is generated, providing the SOA with gain insensitivity to the polarization state of light. In simulations, the SOA with ridge widths of 4 µm, 5 µm, and 6 µm is investigated. A 3 dB gain bandwidth of >140 nm is achieved with a 4 µm ridge width, whereas a 6 µm ridge width provides more output power and gain. The saturated output power is 150 mW (21.76 dB gain) at an input power of 0 dBm but increases to 233 mW (13.67 dB gain) at an input power of 10 dBm. The polarization sensitivity is <3 dBm at −20 dBm. This design, which achieves low polarization sensitivity, a wide gain bandwidth, and high gain, will be applicable in a wide range of fields following further optimization.