One of the most important outcomes of the experiments at the LHC is the Higgs mass, which turned out to be slightly heavier than naive expectation in the Minimal Supersymmetric Standard Model (MSSM). It might imply that the stop masses are heavy and the Higgs sector is fine-tuned. However, an alternative possibility is that there is an additional singlet supermultiplet and the Higgs mass is raised with a new F-term potential and/or a mixing with the singlet. In this case, it is still possible to consider the case that all the particles that are related to the Higgs sector are lighter than 1TeV. Thus we concentrate on this possibility. We examine a general extension of the MSSM with one singlet (General NMSSM.) Especially we consider the case that the Higgs mass is raised mainly by the mixing effects. This is one of the most interesting regions of the general NMSSM because another boson is discoverable and the Higgs signal strengths are deviated from the standard model expectations. Furthermore the mixing effect is \tan\beta insensitive, whereas the F-term contribution is large only in the low \tan\beta region. With the above setup, we find that the higgsinos tend to be light especially at large \tan\beta. Thus the parameter region is further constrained by the LEP search for charginos. Combining this and the LHC constraints on the Higgs signal strengths, we observe that the mixing angles are much constrained and the future measurements of the Higgs signal strengths can cover much of the parameter region. Our result is applicable to a more specific case such as the Z_3 invariant NMSSM and the nearly-MSSM. The only difference is that there are additional constraints on the parameter space.