We experimentally demonstrated, for, it is believed, the first time, high-capacity polarization- and mode-division multiplexing free-space optical transmission with adequate strong turbulence resiliency. A compact spatial light modulator-based polarization multiplexing multi-plane light conversion module was employed to emulate strong turbulent links. By employing advanced successive interference cancellation multiple-input multiple-output decoder and redundant receive channels, the strong turbulence resiliency was significantly improved in a mode-division multiplexing system. As a result, we achieved a record-high line rate of 689.2 Gbit/s, channel number of 10, and net spectral efficiency of 13.9 bit/(s Hz) in a single-wavelength mode-division multiplexing system with strong turbulence.