We study normal forms of germs of singular real-analytic Levi-flat hypersurfaces. We prove the existence of rigid normal forms for singular Levi-flat hypersurfaces which are defined by the vanishing of the real part of complex quasihomogeneous polynomials with an isolated singularity at 0 ∈ C2. This result extends previous results of Burns and Gong (Am J Math 121(1):23–53, 1999) and Fernández-Pérez (Ann Sc Norm Super Pisa Cl Sci (5) XIII:745–774, 2014). Furthermore, we prove the existence of two new rigid normal forms for singular real-analytic Levi-flat hypersurfaces which are preserved by a change of isochore coordinates, that is, a change of coordinates that preserves volume.