We propose a simple phenomenological model for quantum tunneling of Cooper pairs based on their boson like nature. Thus applies to the low energy regime i.e. in the absence of quasiparticle excitations. Around zero bias voltage, our model reveals a rapid increase in tunneling current, which rapidly saturates. This manifests as a zero bias conductance peak that strongly depends on the superconductor´s transition temperature. This low energy tunneling of Cooper pairs could serve as an alternative explanation for a number of tunneling experiments where zero bias conductance peak has been observed.