The neoclassical transport theory in a presence of the temperature anisotropy in the equilibrium distribution function is developed in a large aspect-ratio tokamak. Using a model collision operator, the transport coefficients for the cross-field fluxes and the bootstrap current are explicitly calculated in the banana regime. The electron perpendicular (parallel) heating is found to increase (decrease) the cross-field particle and energy fluxes of electrons and the bootstrap current. The cross-field energy flux of ions are increased (decreased) by the perpendicular (parallel) ion heating. The cross-field fluxes and the bootstrap current are also shown to have the component proportional to the radial electric field.