The interaction of free electrons with intense laser beams in vacuum was st
udied using 3D test particle simulation instead of analytically solving the
relativistic Newton-Lorentz equation of motions. We found a,group of solut
ions for the equation, which reveal very interesting and unusual characteri
stics different from any previously reported. The fundamental characteristi
cs of those trajectories are that an electron can be captured into the high
-intensity region, rather than expelled from it and that the captured elect
ron can be accelerated to GeV energy with an acceleration gradient of 1-50
GeV/cm. These solutions emerges only when the laser intensity is ao greater
than or similar to 100, where a(0) equivalent to eE(0)/m(e)omegac is a mea
sure of the laser intensity. The accelerated GeV electron bunch is a macrop
ulse composed of multiple micropulses, which is analogous to the structure
of bunches produced by conventional linacs. The paraxial approximation equa
tions for the Gaussian laser beam used in the simulation are highly accurat
e and the contribution of the high-order correction is almost negligible wh
en the laser beam width is omega (0) greater than or equal to 60.