Acceleration of electrons by a circularly polarized laser pulse in the presence of a short duration intense axial magnetic field has been studied. Resonance occurs between the electrons and the laser field for an optimum magnetic field leading to effective energy transfer from laser to electrons. The value of optimum magnetic field is independent of the laser intensity and decreases with initial electron energy. The electrons rotate around the axis of the laser pulse with small angle of emittance and small energy spread. Acceleration gradient increases with laser intensity and decreases with initial electron energy.