In this paper, we show the Yau’s gradient estimate for harmonic maps into a metric space (X, dX ) with curvature bounded above by a constant κ (κ 0) in the sense of Alexandrov. As a direct application, it gives some Liouville theorems for such harmonic maps. This extends the works of Cheng (1980) and Choi (1982) to harmonic maps into singular spaces.