The gain characteristics of a semiconductor optical amplifier (SOA) that contains forty layers of closely stacked InAs/GaAs quantum dots (QDs) were studied by employing a fiber-to-fiber measurement system. The fiber-to-fiber gain values obtained for transverse-electric (TE)- and transverse-magnetic (TM)-polarized optical input signals exhibited their maxima at a wavelength of 1100 nm, which corresponds to the excited-state of the closely stacked QDs. In the wavelength range from 1060 to 1170 nm, the gain obtained for TE-polarized input signal was slightly higher than that for TM-polarized input signal and the absolute gain difference was less than 1 dB for an injection current of 80 mA. The small but non-zero difference of the gain reflects the polarization anisotropy of the optical gain provided by the closely stacked QDs. Our results suggest that closely stacked QDs are suitable for realizing polarization-insensitive SOA device with operation bandwidths of more than 100 nm.