Aiming at the poor bit error rate (BER) performance of spinal code in free-space optical communication, a polar-UEP (unequal error protection) spinal concatenated coding scheme for free-space optical communication is proposed. This work combines the unequal error protection characteristics of spinal codes and the construction characteristics of polar codes, using bit sorting and interleaving, to give the best protection of the polar code's information bits, and the bits that are prone to error. Simulation results show that the bit error rate performance of the more important bits and the less important bits of the polar-UEP spinal concatenated code is better than that of the spinal code. When the turbulence intensity is 0.1, compared with the fixed rate coding scheme such as the polar code, the concatenated code generates 0.7 dB-1.2 dB gain at a BER of 10-4. Besides, its BER under different turbulence intensity is lower than that of the spinal code and polar code, and this provides a solution for the efficient application of the spinal code in free-space optical communication.