We analyze 4.5, 8, and 24 μm band Spitzer images of six gamma-ray burst host galaxies at redshifts close to 1. We constrain their star formation rates (SFRs) based on the entire available spectral energy distribution rather than the 24 μm band only. Further, we estimate their stellar masses (M*) based on rest-frame K-band luminosities. Our sample spans a wide range of galaxy properties: derived SFRs range from less than 10 to a few hundred solar masses per year; values of M* range from 109 to 1010 Msolar with a median of 5.6×109 Msolar. Comparing the specific star formation rate (φ≡SFR/M*) of our sample as a function of M* to other representative types of galaxies (distant red galaxies, Lyα emitters, Lyman break galaxies, submillimeter galaxies, and z~2 galaxies from the Great Observatories Origins Deep Survey-North field), we find that gamma-ray burst hosts are among those with the highest φ. This work is based in part on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA.