In this paper, a novel, to the best of our knowledge, signal demodulation algorithm is proposed for the problem of severe scintillation of the received optical irradiance due to turbulence in ultraviolet (UV) communication scenarios. The algorithm innovatively proposes a signal probability model based on the UV turbulence characteristic and derives the optimal solution with dual judgment thresholds. The algorithm can provide a low bit error rate (BER) in scenarios with long distances and large elevation angles and solves the problem of severe degradation of demodulating performance of traditional algorithms, especially in a moderate and strong turbulence channel. A UV LED-based off-line experimental communication system capable of kilometer-scale transmission is established, and the system performance using the algorithm is validated in a 1000 m scenario for the first time to our knowledge and compared with typical traditional demodulation schemes. The results show that the algorithm proposed in this paper has a strong ability to resist the influence of atmospheric turbulence, as it reduces the BER by nearly four orders of magnitude relative to the traditional demodulation algorithm. It effectively improves the performance of UV communication in a strong turbulence scenario.