As　an　effective　approach　for　multi-input　multi-output　regression　estimation　problems,　a　multi-dimensional　support　vector　regression　(SVR),　named　M-SVR,　is　generally　capable　of　obtaining　better　predictions　than　applying　a　conventional　support　vector　machine　(SVM)　independently　for　each　output　dimension.　However,　although　there　are　many　generalization　error　bounds　for　conventional　SVMs,　all　of　them　cannot　be　directly　applied　to　M-SVR.　In　this　paper,　a　new　leave-one-out　(LOO)　error　estimate　for　M-SVR　is　derived　firstly　through　a　virtual　LOO　cross-validation　procedure.　This　LOO　error　estimate　can　be　straightway　calculated　once　a　training　process　ended　with　less　computational　complexity　than　traditional　LOO　method.　Based　on　this　LOO　estimate,　a　new　model　selection　methods　for　M-SVR　based　on　multi-objective　optimization　strategy　is　further　proposed　in　this　paper.　Experiments　on　toy　noisy　function　regression　and　practical　engineering　data　set,　that　is,　dynamic　load　identification　on　cylinder　vibration　system,　are　both　conducted,　demonstrating　comparable　results　of　the　proposed　method　in　terms　of　generalization　performance　and　computational　cost.