The study of nonlinear absorption has potential applications as saturable absorption and optical limiting character in scientific and engineering technology. In this work, we report on the Gaussian vortex beam z-scan to study the saturable absorption in the two-level model. For a given material and laser beam parameters, even though vortex beam shows less saturable absorption nature than the conventional Gaussian beam but not much appreciated. The open aperture z-scan peak is narrower for Gaussian vortex beam as compared with Gaussian beam. Also, in the presence of pico- and femto-second laser pulses, the central dark core of Gaussian vortex beam can provide a stable and accurate z-scan profile with avoiding thermal and other nonlinear optical effects at the beam waist of z-scan in the saturable absorber characterization. With including above mentioned points, we have shown how the Gaussian vortex z-scan is superior to the conventional Gaussian beam z-scan for saturable absorber characterization. Though discussed for single-photon absorption, it may extend to multi-photon absorption.