Far-infrared magneto-optical experiments have been performed on a n-type 90-\AA{}-HgTe/40-\AA{}-CdTe superlattice. We have observed three electron cyclotron resonances which are remarkably resolved by increasing temperature. Through the studies of selection rules, temperature effects and k\ensuremath{\cdot}p band calculations, they have been identified as three inter-Landau level transitions occurring in an electronic subband c1 for the value of --- valence-band offset --- \ensuremath{\Lambda}\ensuremath{\simeq}40 meV. Calculations show that, for our particular layer thicknesses, the sample should be semimetallic for \ensuremath{\Lambda}\ensuremath{\simeq}350 meV where its linear in-plane energy dispersion gives very different magneto-optical behaviors from those for \ensuremath{\Lambda}\ensuremath{\simeq}40 meV. The successful fit of data for \ensuremath{\Lambda}\ensuremath{\simeq}40 meV, but the failure for \ensuremath{\Lambda}\ensuremath{\simeq}350 meV, provides evidence for a small valence-band offset in HgTe/CdTe superlattice.