  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 $B \parallel a,b$ and shows a strong anisotropy $B_{c2}^{a}
\simeq B_{c2}^{b} \gg B_{c2} ^{c}$. This provide 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 $m_0 = 0.07 \mu_{B}$. An unusual curvature or kink is
observed in the temperature variation of $B_{c2}$, which possibly indicates
UCoGe is a two-band ferromagnetic superconductor.
