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In this work we apply the Gutzwiller theory for various models for LaOFeAs. It was discovered in 2008 that doped LaOFeAs is superconducting below a temperature of Tc=28 K. Soon after that discovery, more iron based materials were found which have an atomic structure that is similar to the one of LaOFeAs and which are also superconducting. These materials form the class of iron-based superconductors. Many properties of this material class are in astonishing agreement with the properties of the cuprates. Therefore, studying this new material may promote our understanding of high-Tc superconductivity. Despite great efforts, however, Density Functional Theory calculations cannot reproduce the small magnetic moment in the ground state of undoped LaOFeAs. Such calculations overestimate the magnetic moment by a factor 2-3. Within our Gutzwiller approach, we take additional local Coulomb correlations into account. We show that it is necessary to work with the iron 3d-orbitals and the arsenic 4p-orbitals to obtain a realistic description of LaOFeAs. For a broad parameter regime of the electronic interactions, we find a magnetic moment that is in the region of the experimentally observed values. We claim that the magnetic phase in LaOFeAs can be described as a spin-density wave of Landau-Gutzwiller quasi-particles.