In this paper we consider the movement of an electron in the single electron tunnel process through a mesoscopiccapacitor. The results show that, due to the Coulomb force, there is a threshold voltage Vt in the mesoscopic LC circuit.When the external voltage is lower than the threshold voltage, the tunnel current value is zero, and the Coulomb blockadephenomenon arises. Furthermore, considering that the mesoscopic dimension is comparable to the coherence length inwhich charge carriers retain the phase remembrance, a weak coupling can be produced through the proximity effectof the normal metal electrons of both electrodes of a mesoscopic capacitor. By varying the external voltage, we canobserve the Shapiro current step on the current-voltage characteristic curve of a mesoscopic LC circuit.