  We present a simple supersymmetric axion model that can naturally explain the
origin of the Higgs mu and Bmu terms in gauge mediation while solving the
strong CP problem. To stabilize the Peccei-Quinn scale, we consider mixing
between the messenger fields that communicate the supersymmetry and
Peccei-Quinn symmetry breaking to the visible sector. Such mixing leads to the
radiative stabilization of the Peccei-Quinn scale. In the model, a Higgs
coupling to the axion superfield generates the B parameter at the soft mass
scale while a small mu term is induced after the Peccei-Quinn symmetry
breaking. We also explore the phenomenological and cosmological aspects of the
model, which crucially depend on the saxion and axino interactions with the
ordinary particles induced by the Higgs coupling to the axion superfield.
