We report single-mode, surface-emitting, mid-IR, photonic-crystal (PhC), quantum-cascade lasers with linearly polarized and highly directional single-lobed emission. A metallic square-lattice photonic crystal with elliptical air holes and pi phase shift was used as the resonator. The 2D feedback coupling--necessary for the operation of the photonic-crystal resonator--is induced by the mismatch between the modes supported by metalized and nonmetalized regions and yields single-mode output with a side-mode suppression ratio >30 dB. The elliptical air holes modify the relative intensities of the TM field components (H(x) and H(y)) in the PhC plane, thus yielding linearly polarized emission. The pi phase shift allows the system to produce a single-lobed pattern in the far field with a narrow divergence angle (2.4 degrees x 1.8 degrees). The emission is perfectly orthogonal to the device surface, and the maximum operating temperature--still limited by the metallic ohmic losses--is 240 K.