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 : the angular size of the sound horizon at recombination , the Thomson scattering optical depth due to reionization , the physical densities of baryons and cold dark matter , and the scalar spectral index are estimated to be \theta _ { * } = ( 1.0415 ^ { +0.0012 } _ { -0.0011 } ) \times 10 ^ { -2 } , \tau = 0.0914 ^ { +0.0266 } _ { -0.0242 } , \Omega _ { b } h ^ { 2 } = 0.0222 \pm 0.0005 , \Omega _ { c } h ^ { 2 } = 0.1177 \pm 0.0036 , and n _ { s } = 0.9644 ^ { +0.0118 } _ { -0.0119 } , respectively , at 95 % confidence level ( CL ) . 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 .