We describe a general method to compute the Z2-Thurston norm for every Z2-homology class in an orientable Seifert manifold with orientable orbit surface. Our main tools are pseudo-horizontal surfaces. We give a necessary and sufficient criterion for the existence of pseudo-horizontal surfaces, calculate the non-orientable genera for such surfaces, and detect their Z2-homology classes. We then describe an algorithm to calculate the Z2-Thurston norm of each Z2-homology classes. We also present several interesting examples.