The absolute neutrino mass scale is currently unknown, but can be constrained by cosmology. The WiggleZ high redshift, star-forming, and blue galaxy sample offers a complementary data set to previous surveys for performing these measurements, with potentially different systematics from nonlinear structure formation, redshift-space distortions, and galaxy bias. We obtain a limit of ∑m_ν<0.60 eV (95% confidence) for WiggleZ+Wilkinson Microwave Anisotropy Probe. Combining with priors on the Hubble parameter and the baryon acoustic oscillation scale gives ∑m_ν<0.29 eV, which is the strongest neutrino mass constraint derived from spectroscopic galaxy redshift surveys
