Multiple-input-multiple-output （MIMO） and non-orthogonal multiple access （NOMA） techniques are widely applied to unmanned aerial vehicle （UAV） communications due to their superior spectral efficiency. UAVs can serve as relays to provide flexible and reliable connections for users， thereby adding significant research value. To overcome the problems of multi-user interference and clustering in the MIMO-NOMA UAV relay networks， a new downlink transmission model based on amplify-and-forward （AF） is proposed. First， a three-dimensional stochastic geometry framework is applied to user clustering， and an AF-based precoding scheme is proposed according to the NOMA principle. Second， the analytical expressions for the outage probability （OP） of paired users are derived following the statistics of the equivalent propagation channel of AF relay transmitting model. And the asymptotic results and diversity order of OP under high signal-to-noise ratio （SNR） are obtained using the first-order Taylor expansion. Finally， simulations validate the theoretical analysis results through the impact of key variables on OP performance. Additionally， compared with existing transmission schemes in MIMO-NOMA， the proposed scheme can effectively improve the OP performance in multiple user UAV relay networks.