  To solve the $\mu$ problem of the MSSM, the $\mu$ from $\nu$ Supersymmetric
Standard Model ($\mu\nu$SSM) introduces three singlet right-handed neutrino
superfields $\hat{\nu}_i^c$, which lead to the mixing of the neutral components
of the Higgs doublets with the sneutrinos, producing a relatively large CP-even
neutral scalar mass matrix. In this work, we analytically diagonalize the
CP-even neutral scalar mass matrix and analyze in detail how the mixing impacts
the lightest Higgs boson mass. We also give an approximate expression for the
lightest Higgs boson mass. Simultaneously, we consider the radiative
corrections to the Higgs boson masses with effective potential methods.
