We present Spitzer /IRAC 4.5 \mu m transit photometry of GJ 3470 b , a Neptune-size planet orbiting a M1.5 dwarf star with a 3.3-day period recently discovered in the course of the HARPS M-dwarf survey . We refine the stellar parameters by employing purely empirical mass-luminosity and surface brightness relations constrained by our updated value for the mean stellar density , and additional information from new near-infrared spectroscopic observations . We derive a stellar mass of M _ { \star } = 0.539 ^ { +0.047 } _ { -0.043 } M _ { \odot } and a radius of R _ { \star } = 0.568 ^ { +0.037 } _ { -0.031 } R _ { \odot } . We determine the host star of GJ 3470 b to be metal-rich , with a metallicity of { [ Fe / H ] } = +0.20 \pm 0.10 and an effective temperature of T _ { eff } = 3600 \pm 100 K. The revised stellar parameters yield a planetary radius R _ { p } = 4.83 _ { -0.21 } ^ { +0.22 } R _ { \oplus } that is 13 % larger than the value previously reported in the literature . We find a planetary mass M _ { p } = 13.9 ^ { +1.5 } _ { -1.4 } M _ { \oplus } that translates to a very low planetary density , \rho _ { p } = 0.72 ^ { +0.13 } _ { -0.12 } g cm ^ { -3 } , which is 33 % smaller than the original value . With a mean density half of that of GJ 436 b , GJ 3470 b is an example of a very low-density low-mass planet , similar to Kepler-11 d , Kepler-11 e , and Kepler-18 c but orbiting a much brighter nearby star that is more conducive to follow-up studies .