The linearly polarized single photon is a key component for single-photon applications, such as quantum simulators and quantum key distribution. Here, we propose a novel approach for generating linearly polarized single photons using a simple elliptic mesa containing an InAs/GaAs quantum dot (QD). We found that 91% of the QD emission can be linearly polarized along the major axis for an elliptic mesa with a minor axis diameter of 300 nm. The degree of linear polarization of the QD emission was studied with the polarization mode distribution in the QD layer of the elliptic mesa by finite-difference time-domain simulations. The mode polarized along the major axis was dominant over the mesa plane, especially in the center for the 300 nm mesa, enabling high linear polarization of single photons emitted from the mesa. The proposed method for generating linearly polarized single photons using a simple elliptic mesa, which features a broad operation band and can be easily fabricated, will be potentially useful in numerous single-photon applications.