An approximate expression for the beam driven current in which the trapping effects of fast ions and electrons are included is derived by means of a variational principle. The beam driven current due to arbitrary fast ions can be calculated easily from this expression in an axisymmetric magnetic field with finite aspect ratio. It is shown that in a tokamak with circular cross-section this expression gives a good approximation to the results obtained by numerically solving the Fokker-Planck equation. The beam driven current due to energy diffusion, which is neglected in the approximate expression, is also estimated