Abstract: Let ℋ be a t-regular hypergraph on n vertices and m edges. Let M be the m × n incidence matrix of ℋ and let us denote λ = max_{v ∈ 𝟏^⟂} 1/‖v‖ ‖Mv‖. We show that the discrepancy of ℋ is O(√t + λ). As a corollary, this gives us that for every t, the discrepancy of a random t-regular hypergraph with n vertices and m ≥ n edges is almost surely O(√t) as n grows. The proof also gives a polynomial time algorithm that takes a hypergraph as input and outputs a coloring with the above guarantee.