Non-line-of-sight ultraviolet communication can be competent for complex environment and special terrain. However, atmospheric absorption, scattering and turbulence can result in rapid attenuation of signal intensity, which greatly limits the transmission distance. Cooperative relay is an effective method to overcome this shortcoming and expand the communication range. For the non-coplanar relay assisted ultraviolet scattering system in atmospheric turbulence, the closed-form expressions of outage probability under decode-and-forward (DF) protocol as well as amplify-and-forward (AF) protocol are derived. The correctness of the theoretical analysis results is verified through Monte Carlo simulation. The simulation results show that the outage performance of DF is better than that of AF. And the higher the optical transmission power, the smaller the receiving elevation and the offset angle, the better the outage performance of the system. Moreover, the change rule of outage probability with transmission elevation is different when the offset angle is different.