Let (X, d, μ) be a metric measure space with non-negative Ricci curvature. This paper is concerned with the boundary behavior of harmonic function on the (open) upper half-space . We derive that a function f of bounded mean oscillation (BMO) is the trace of harmonic function on , whenever u satisfies the following Carleson measure condition
where denotes the total gradient and denotes the (open) ball centered at with radius . Conversely, the above condition characterizes all the harmonic functions whose traces are in BMO space.