We study the asymptotic behavior of d-dimensional Brownian Motion in unbounded incompressible random flows. We strengthen previous results (Oelschläger (1988), Fannjiang and Papanicolaou (1995)) and simplify the proof of the invariance principle in the sense of almost sure convergence in law by means of the martingale method. The key estimate is obtained by the PDE method called Moser's iterative scheme.