We report upper critical field B(c2)(T) measurements on a single-crystalline sample of the ferromagnetic superconductor UCoGe. B(c2)(0) obtained for fields applied along the orthorhombic axes exceeds the Pauli limit for B parallela,b and shows a strong anisotropy B(c2)(a) approximately B(c2)(b)>>B(c2)(c). This provides evidence for an equal-spin pairing state and a superconducting gap function of axial symmetry with point nodes along the c axis, which is also the direction of the uniaxial ferromagnetic moment m(0)=0.07micro(B). An unusual curvature or kink is observed in the temperature variation of B(c2) which possibly indicates UCoGe is a two-band ferromagnetic superconductor.