  We wish to investigate whether there is an extension to the base $\Lambda$CDM
cosmology that can resolve the tension between the Planck observation of the
cosmic microwave background anisotropies and the local measurement of the
Hubble constant. We consider various plausible extended models in this work,
and we use the Planck 2015 observation, combined with the baryon acoustic
oscillation data, the JLA type Ia supernovae data, and the local measurement of
the Hubble constant (by Riess et al. in 2016), to make an analysis. We find
that the holographic dark energy plus sterile neutrino model can reduce the
tension to be at the 1.11$\sigma$ level, but this model is obviously not
favored by the current observations. Among these extended models, the
$\Lambda$CDM+$N_{\rm eff}$ model is most favored by the current observations,
and this model can reduce the tension to be at the 1.87$\sigma$ level. By a
careful test, we conclude that none of these extended models can convincingly
resolve the $H_0$ tension.
