A kinetic equation is derived for the neoclassical distribution function of alpha particles with orbits intersecting or approaching the magnetic axis of a tokamak. This equation takes into account both the collisional slowing down and the pitch-angle scattering of alpha particles. An equation with a simplified pitchangle scattering term is solved analytically, and the distribution function obtained is used to find the alpha-particle bootstrap current at the magnetic axis. It is shown that the pitch-angle scattering leads to an alpha-particle current in the near-axis region that is larger than the one predicted from early neoclassical theory, which allows only for the slowing down of alpha particles.