A strengthening method using a thin layer composed of longitudinally expanded steel mesh (ESM) and high-performance mortar is proposed to meet the principles of “minimal intervention” and “material compatibility” in the strengthening of concrete components for historical buildings. An experimental study was conducted on reinforced concrete columns with a designated concrete strength of C20. These columns was strengthened using the afore-mentioned method under small eccentric compression loading. The test results show that an increase in the number of steel mesh layers and the thickness of the strengthening mortar can significantly improve the bearing capacity and the ductility of the specimens. The cracks that appeared in the strengthening mortar when the specimen failed were mainly concentrated on the compression surface, the corners of the compression zone, and the two sides near the compression zone. This indicates that the strengthening layer has a significant confinement effect on the concrete in the compression zone. Considering the improvement effect of ESM and high-performance mortar on the compressive strength of constrained concrete, a limit state analysis was conducted on the strengthened columns under small eccentric compression, and the calculated values of their ultimate capacity were in good agreement with the experimental ones.