We study a variation to the SUSY Left–Right symmetric model based on the gauge group SU(3)C×SU(2)L×SU(2)R×U(1)BL. Beyond the quark and lepton superfields we only introduce a second Higgs bidoublet to produce realistic fermion mass matrices. This model does not include any SU(2)R triplets. We calculate renormalization group evolutions of soft SUSY parameters at the one-loop level down to low energy. We find that an SU(2)R slepton doublet acquires a negative mass squared at low energies, so that the breaking of SU(2)R×U(1)BL→U(1)ᵧ is realized by a non-zero vacuum expectation value of a right-handed sneutrino. Small neutrino masses are produced through neutrino mixings with gauginos. Mass limits on the SU(2)R×U(1)BL sector are obtained by direct search results at the LHC as well as lepton-gaugino mixing bounds from the LEP precision data.