The authors investigate the vacuum stability conditions of the supersymmetric reduced minimal 331 model (SUSYRM331) that create important consequences on Higgs mass spectrum as well as soft-parameters of the model. the authors prove that if this condition is satisfied then all Higgses are massive. Furthermore, soft-parameters should be in order of SU(3)L scale. Based on this, the authors investigate in detail masses of CP-even neutral and doubly charged Higgses in the model. The neutral Higgs sector includes one light Higgs with mass at tree level m H0-1 ~ mZ |COB 2gama| 92.0 Ge V and three other heavy Higgses. For doubly charged Higgses, there may exist a light Higgs which can be observed by recent colliders such as LHC.