C.~Fefferman and E.~M.~Stein proved the interpolation theorem between $L^p$ and $BMO$. The purpose of this paper is to consider the analogue of the above theorem of C.~Fefferman and E.~M.~Stein, i.e. the interpolation theorem between $B_0^p$ and $BMO$, by means of the properties of the sharp function $f^{\sharp}$ and the duality that the space $CMO^p$ is the dual space to ${HA}^{p'}$, $1/p + 1/{p'} = 1$.