The vectorial properties of paraxial beams propagating along the optical axis of uniaxial left-handed materials are studied. On the basis of a suitable plane-wave angular spectrum representation of the electromagnetic field, we obtain the analytical expressions of the optical field. The longitudinal component is expressible in terms of the firest correction of the transverse field. Moreover, the transverse field varies when either of the polarization and the distributing of the initial electromagnetic field is changed. But the longitudinal component is only dependent on the initial distributing of the field.