By using the generalized Huygens Fresnel diffraction integral, the focusing of high power laser beams with amplitude modulations and phase fluctuations passing a lens with a central obstruction aperture has been studied in detail. The beam focusability in the focal plane has been discussed. Numerical calculation results show the dependence of the power (energy) focusability on the obstruction ratio, truncation parameter, the amplitude modulation and phase fluctuation parameters.