For the dual-hop relay system of unmanned aerial vehicle (UAV), a propagation loss model of dual-hop relay link is established. The influence of fuselage feature, antenna characteristics, climate condition and channel fading are considered. Based on the model, the calculating methods of propagation loss are analyzed. Then the statistical characteristics of propagation loss with random fluctuation caused by composite fading including shadowing and multipath fading are derived. Furthermore, the theoretical expression of the outage probability and bit error rate (BER) of dual-hop UAV relay system is developed. Finally, through the numerical simulations in urban, mountainous and sea, the theoretical results accuracy obtained is verified and the impact of flight altitude, ground node position and communication scenarios on the performance of the dual-hop relay system is discussed.