Hermite–Gaussian (HG) beam has enormous potential to enhance the capacity of free-space optical (FSO) communication due to its unique orthogonal spatial modes. However, the combined influence of atmospheric turbulence and pointing error on average irradiance for a mobile FSO link have rarely been reported before. The closed form of average irradiance of an HG beam under an arbitrary magnitude pointing error in atmospheric turbulence is deduced through a statistical averaging method. The accuracy of the proposed theoretical results was verified by a phase screen simulation. We found that the average irradiance profile of an HG beam finally changes into an approximate Gaussian shape with the increase of atmospheric turbulence and pointing error, and the larger beam waist can mitigate the profile change with an increase of atmospheric turbulence and pointing error. Based on the expressions of average irradiance, the effective spot size and average received power under the pointing error in atmospheric turbulence were derived and analyzed. This research provides the fundamental theoretical expressions for performance research on an HG beam-based mobile FSO link in atmospheric turbulence.