  Based on the simple phenomenological $\sigma \pi \pi$, $\sigma N N$ and $\pi
\pi \gamma$ interactions, we estimate the $\sigma$ exchange effect in the Lamb
shift of muonic hydrogen. We at first calculate the effective couplings of
$\sigma\mu\mu$ by two photons and two pions exchange, then calculate the
corresponding corrections to the energy shift of the 2S/2P states of muonic
hydrogen. We find the correction to the energy shift of 2S state is about
-14$\mu$eV by the current used parameters, which is about $44\%$ of the usual
two photons exchange contribution, and is larger than the current experimental
precision, and should be considered in the experimental analysis.
