Abstract: Active 3D reconstruction of moving objects requires selecting informative viewpoints while accounting for object motion during the decision-to-execution delay. However, most next-best-view (NBV) planners assume static objects, while motion-aware active perception for moving targets typically prioritizes tracking over surface coverage. We present a motion-uncertainty-aware NBV framework for reconstructing an unknown rigid object undergoing planar translation, using only noisy planar position measurements of the object and depth observations from a separate mobile robot. Our key idea is to plan over a predictive distribution of future camera-object configurations. We maintain a predictive object-state belief over planar position and velocity using a fixed-lag Gaussian Process smoother, propagate it one step forward, and generate candidate viewpoints around the predicted object location. We filter candidates by single-step reachability, then evaluate feasible viewpoints by expected coverage gain under the predictive belief via Monte Carlo sampling of induced camera-object configurations, and execute the highest-utility feasible view. Simulations and real-world experiments demonstrate improved surface coverage and reconstruction completeness over non-predictive and tracking-only baselines, bridging tracking-driven prediction and coverage-driven NBV.