In this article, a 1x12 millimeter-wave (mmW) linearly tapered slot antenna (LTSA) array, fed by high-order waveguide modes, is introduced. Due to the antiphase characteristic between adjacent channels of a power divider based on the TE2n,0 mode waveguide, the cross-polarized E-field components can cancel each other out in an end-fire direction, even in the case of a relatively thick substrate. Moreover, the electric separations between the adjacent channels employed in a traditional substrate integrated waveguide (SIW) power divider can be removed without affecting the field distributions. This facilitates in improving robustness to avoid fabrication errors. Additionally, a general condition of generating a single high-order mode with symmetrical protection is outlined. By combining two antiphase TE30 mode waveguides, an equivalent TE60 mode waveguide with six identical output channels is realized. To feed a 12-element array, two equivalent TE60 mode waveguides are employed as an equivalent TE12,0 mode-feeding network. Instead of the complex 1-to-n-way power divider and relatively thin substrate featured in previous works, the high-order mode-fed LTSA array introduced in this study is able to operate over 26.5b-30 GHz with substrate height of 2 mm (0.19λ0), yielding a cross-polarization level of less than -15 dB.