The Mg-enriched magnesium aluminum silicate (MAS) glass is known for its higher mechanical strength and chemical resistance. Among such glasses, cordierite ($Mg_2Al_4Si_5O_{18}$) is well known to have a low thermal expansion and low melting point. Polycrystalline engineering ceramics such as alumina can be strengthened by a surface modification with low thermal expansion materials. The present study involves the synthesis of cordierite by a sol-gel process and investigates the effect of glass penetration on the surface of alumina. The cordierite powders were prepared from $Al(OC_3H_7)_3$, $Mg(OC_2H_5)_2$ and tetraethyl orthosilicate by hydrolysis and condensation reaction. The cordierite powders were characterized by X-ray diffraction (XRD, Rigaku), scanning electron microscope (SEM, JEOL: JSM-5610), energy dispersive spectroscopy (EDS, JEOL: JSM-5610), and universal testing machine (UTM, INSTRON). The X-ray diffraction patterns showed that the synthesized particles were ${mu}$-cordierite calcined at $1100^{circ}C$ for 1 h. The shape of synthesized cordierite was changed from ${mu}$-cordierite to ${alpha}$-cordierite with increasing calcination temperature. Synthesized cordierite was used for surface modification of alumina. Cordierite powders penetrated deeply into the alumina sample along grain boundaries with increasing temperature. The results of surface modification tests showed that the strength of the prepared alumina sample increased after surface modification. The strength of a surface modified with synthesized cordierite increased the most, to about 134.6MPa.