We give a Fekete-Szegö type inequality for a Bloch function with Bloch seminorm ≤ 1. As an application of it, we derive a sharp coefficient inequality for a3 for a uniformly locally univalent function f(z)=z+a2z2+a3z3+... on the unit disk with pre-Schwarzian norm ≤ λ for a given λ>0.