We found that the conventional model of orbital-ordering of 3x(2)-r(2)/3y(2)-r(2) type in the e(g) states of La0.5Sr1.5MnO4 is incompatible with measurements of linear dichroism in the Mn 2p-edge x-ray absorption, whereas these e(g) states exhibit predominantly cross-type orbital ordering of x(2)-z(2)/y(2)-z(2). LDA+U band-structure calculations reveal that such a cross-type orbital-ordering results from a combined effect of antiferromagnetic structure, Jahn-Teller distortion, and on-site Coulomb interactions.