In this paper we study the propagation of the single cycle or much shorter pulsed-beam in free space. We show the invalidation of the slowly-varying envelope approximation (SVEA) theory because it leads to the spatial singularity of the ultrashort pulsed-beam solution and is inconsistent with the physical significance of the beam propagation. We eliminate the spatial singularity by making use of the complex analytical signal theory (CAS), and then give the solution and simulation of the Gauss, hyperbolic secant and Lorentz pulse beam for SVEA and CAS. The SVEA and CAS solutions are consistent if the pulsed beam becomes long enough.