The Glauber theory has been used to investigate the reaction cross section of proton-rich nucleus $^{23}$Al. A core plus a proton structure is assumed for $^{23}$Al. HO-type density distribution is used for the core while the density distribution for the valence proton is calculated by solving the eigenvalue problem of Woods-Saxon potential. The transparency function in an analytical expression is obtained adopting multi-Gaussian expansion for the density distribution. Coulomb correction and finite-range interaction are introduced. This modified Glauber model is apt for halo nuclei. A dominate s-wave is suggested for the last proton in $^{23}$Al from our analysis which is possible in the RMF calculation.
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