Inflection-point inflation is an interesting possibility to realize a successful slow-roll inflation when inflation is driven by a single scalar field with its initial value below the Planck mass (phi(1) less than or similar to M-P1). In order for a renormalization group (RG) improved effective lambda phi(4) potential to develop an inflection point, the quartic coupling lambda(phi) must exhibit a minimum with an almost vanishing value in its RG evolution, namely lambda(phi(1)) similar or equal to 0 and beta(lambda)(phi(1)) similar or equal to 0, where beta(lambda). is the beta function of the quartic coupling. As an example, we consider the minimal gauged B - L extended Standard Model at the TeV scale, where we identify the B - L Higgs field as the inflaton field. For a successful inflection-point inflation, which is consistent with the current cosmological observations, the mass ratios among the Z' gauge boson, the right-handed neutrinos and the B - L Higgs boson are fixed. Our scenario can be tested in the future collider experiments such as the high-luminosity LHC and the SHiP experiments. In addition, the inflection-point inflation provides a unique prediction for the running of the spectral index alpha similar or equal to -2.7 x 10(-3)(60/N)(2) (N is the e-folding number), which can be tested in the near future.