The variable Zagreb vM2 index is introduced and applied to the structure-boiling point modeling of benzenoid hydrocarbons. The linear model obtained (the standard error of estimate for the fit model Sfit=6.8 oC) is much better than the corresponding model based on the original Zagreb M2 index (Sfit=16.4 oC). Surprisingly, the model based on the variable vertex-connectivity index (Sfit=6.8 oC) is comparable to the model based on vM2 index. A comparative study with models based on the vertex-connectivity index, edge-connectivity index and several distance indices favours models based on the variable Zagreb vM2 index and variable vertex-connectivity index. However, the multivariate regression with two-, three- and four-descriptors gives improved models, the best being the model with four-descriptors (but vM2 index is not among them) with Sfit=5 oC, though the four-descriptor model contaning vM2 index is only slightly inferior (Sfit=5.3 oC).