This　paper　develops　a　positivity-preserving　and　free　energy　dissipative　hybrid　scheme　for　the　multi-dimensional　Poisson-Nernst-Planck　equations　with　multiple　ions　on　unstructured　polygonal　and　polyhedral　meshes.　It　is　built　on　the　linear　virtual　element　method　for　the　Poisson-type　equation　for　the　electrostatic　potential　and　a　cell-centered　finite　volume　scheme　for　the　Nernst-Planck　equations　for　the　ion　concentrations,　and　preserves　the　positivity　of　the　ion　concentrations,　the　mass　conservation,　the　free　energy　dissipation　and　steady-state　properties.　The　existence　of　the　numerical　solutions　is　also　discussed.　Numerical　results　demonstrate　the　effectiveness　of　the　proposed　two-　and　three-dimensional　schemes.