Improvement of the selectivity of nonenzymatic glucose based on mesoporous platinum ($H_1$-ePt) by using A.C. impedance is reported. The idea of the present work is based on the novel effect of the mesoporous electrode that the apparent exchange current due to glucose oxidation remarkably grows although the reaction kinetics on the surface is still sluggish. It is expected that the enlarged apparent exchange current on the mesoporous electrode can raise the sensitivity of admittance in A.C. impedance to glucose concentration. At a low frequency, A.C. impedance could become more powerful. The admittance at 0.01 Hz is even more sensitive to glucose than to ascorbic acid while amperometry exhibits the inverse order of sensitivity. This is the unique behavior that is neither observed by A.C. impedance on flat platinum electrode nor obtained by amperometry. The study shows how the combination of A.C. impedance and nano-structured surface can be applied to the detection of sluggish reaction such as electrochemical oxidation of glucose.