This paper proposes a novel, U-tree based indexing technique that addresses the problem of managing uncertain data in a constantly evolving environment. The technique called TPU-tree is capable of indexing the moving objects with uncertainty in multi-dimensional spaces. Along with the data models capturing the temporal and spatial uncertainty, a modified p-bound based range query (MP_BBRQ) algorithms for probabilistic queries is also developed. Experimental evaluations demonstrate that the TPU-tree supports queries on uncertain moving objects quite efficiently. It yields rather good update performance even under frequent update environments, and has a practical value.