ABSTRACT The event rate of long gamma-ray bursts (GRBs) is expected to be a useful tracer of cosmic star-formation history. For this purpose, it is necessary to understand what kinds of star formation/galaxies are traced by GRBs. Here we report rest-frame far-infrared (FIR) continuum detections of the GRB 070521 and 080207 host galaxies at z ∼ 2 with Atacama Large Millimeter/submillimeter Array (ALMA) bands 8 and 9. FIR photometry provides reliable star-formation rates (SFRs), because FIR emission is free from dust extinction and possible radio contamination from the long-lived afterglows of GRBs. Spectral energy distribution fitting yields 49.85$^{+72.33}_{-2.86}$ and 123.4$^{+25.19}_{-21.78}$ M⊙ yr−1 for the 070521 and 080207 hosts, respectively. The derived SFRs place them on the ‘main sequence’ of normal star-forming galaxies at z ∼ 2. The derived SFRs are significantly lower than those from radio observations. It is inferred that the observed radio fluxes in a previous study are contaminated by afterglows. ALMA marginally detected the [C ii] 158-μm emission line from the GRB 080207 host galaxy with signal-to-noise ratio (S/N) ∼ 4. This is the first detection of [C ii] 158-μm from a GRB host at z > 2 and the second detection among known GRBs. The luminosity ratio of [C ii] 158 μm to FIR is 7.5 × 10−4, which is one of the smallest values among galaxies at z ∼ 1–2 with the same FIR luminosity. The ‘[C ii] deficit’ could be a new physical property with which to characterize GRB hosts at z ∼ 1–2. Possible parameters controlling the deficit include the metallicity, initial mass function and gas density.