Non-coplanar VMAT treatment can achieve better organ-at-risk (OAR) avoidance by orienting the radiation beams in a different geometric plane relative to the patient. However, determining the optimal set of beam orientations is challenging due to the additional degrees of freedom. The objective of this study was to use Simulated Annealing (SA) for beam selection in noncoplanar VMAT optimization context. SA method was combined with a direct leaf trajectory optimization approach to obtain a set of globally optimal beams which serve as control points for the treatment trajectory. Proposed method was evaluated through the TG119 benchmark and two clinical cases (prostate and liver cancers). Finally, the SA beam selection method was compared to the standard coplanar and non-coplanar beam selection approach. The results showed an accurate delivery of the prescription dose to the target tumor volume in all cases. Generally, not on every organ, the non-coplanar SA method showed better organ-at-risk (OAR) sparing compared to the coplanar and non-coplanar greedy method. This work demonstrates that optimized non-coplanar beam orientations using the proposed SA method can be more clinically interesting than coplanar method in some specific patient cases.