  We investigate a scalar field dark energy model (i.e., $\phi$CDM model) with
massive neutrinos, where the scalar field possesses an inverse power-law
potential, i.e., $V(\phi)\propto {\phi}^{-\alpha}$ ($\alpha>0$). We find that
the sum of neutrino masses $\Sigma m_{\nu}$ has significant impacts on the CMB
temperature power spectrum and on the matter power spectrum. In addition, the
parameter $\alpha$ also has slight impacts on the spectra. A joint sample,
including CMB data from Planck 2013 and WMAP9, galaxy clustering data from
WiggleZ and BOSS DR11, and JLA compilation of Type Ia supernova observations,
is adopted to confine the parameters. Within the context of the $\phi$CDM model
under consideration, the joint sample determines the cosmological parameters to
high precision. It turns out that $\alpha <4.995$ at 95% CL for the $\phi$CDM
model. And yet, the $\Lambda$CDM scenario corresponding to $\alpha = 0$ is not
ruled out at 95% CL. Moreover, we get $\Sigma m_{\nu}< 0.262$ eV at 95% CL for
the $\phi$CDM model, while the corresponding one for the $\Lambda$CDM model is
$\Sigma m_{\nu} < 0.293$ eV. The allowed scale of $\Sigma m_\nu$ in the
$\phi$CDM model is a bit smaller than that in the $\Lambda$CDM model. It is
consistent with the qualitative analysis, which reveals that the increases of
$\alpha$ and $\Sigma m_\nu$ both can result in the suppression of the matter
power spectrum. As a consequence, when $\alpha$ is larger, in order to avoid
suppressing the matter power spectrum too much, the value of $\Sigma m_\nu$
should be smaller.
