There are many defects in the Gaussian model, which is used to describe the far-field distribution of semiconductor lasers. Though the Gaussian distribution is applicable to the description of the far-field distribution parallel to the junction, it is not suitable to describe the far-field distribution perpendicular to the junction. With the same spatial extensions, the angular spreading of the Lorentz-Gauss distribution is higher than that of the Gaussian distribution. Therefore, the Lorentz-Gauss distribution provides more appropriate model than the Gaussian distribution to describe the far-field distribution perpendicular to the junction of semiconductor lasers. However, the researches show that the Lorentz-Gauss beams are only valid for the description of the highly divergent fundamental mode. Moreover, the high power semiconductor lasers also generate the highly divergent higher-order modes. The purpose of this paper is to construct an orthogonal and complete family of higher-order Lorentz-Gauss beams. By analyzing the propagation properties of higher-order Lorentz-Gauss beams, it is proved that higher-order Lorentz-Gauss beams are more appropriate than Hermite-Gauss beams to describe the highly divergent higher-order far-field distribution of semiconductor lasers.