The effect of alkaline-earth ions on Na transport in aluminosilicate glasses was studied by measuring ionic conductivity for a systematic compositional series of Na2O-RO-Al2O3-SiO2 glasses (R=Mg, Ca, Sr, Ba). The Na transport in aluminosilicate glass could be affected by compositional changes in aluminum coordination and nonbridging oxygen as well as physical properties such as dielectric constant, shear modulus, and ionic packing factor. Through careful experimental designs and measurements, the main determinants among these parameters were identified. Al-27 MAS-NMR indicated that all aluminum species contained in these glasses are four-coordinated. The activation energy for ion conductivity decreased with increasing aluminum content and decreasing ionic radii of the alkaline-earth ion in the region where [Al] < [Na]. When the aluminum content exceeded the sodium content ([Al] > [Na]), the composition dependence of the activation energy depended on the specific alkaline earth. These results are explained based on variations in free volume and dielectric constant caused by structural changes around the AlO4 charge compensation sites. These structure changes occur in response to the smaller size and higher field strength of the alkaline-earth ions, and are most prevalent in the compositions which require bridging of two AlO4 sites by the alkaline-earth ion for charge compensation.