We analyze a vacuum structure of the Higgs sector in the Next-to Minimal Supersymmetric Standard Model (NMSSM). We show that some minima, which can be identified as false vacua, can be found analytically along specific directions. These minima can become deeper than the true vacuum or the electroweak symmetry breaking vacuum. Such minima should be avoided to ensure the stability of the true vacuum, resulting in constraints on the parameters of the NMSSM. The masses of the Higgses can be restricted using the constraints. We show that the Higgs masses can not be heavy so much in some parameter regions even in the NMSSM