•Thermal conductivity measurements have been performed from 2 to 330 K on single crystals of pyrochlore R2Ti2O7 (R=Gd, Tb, Dy, Ho, Er, Lu, and Y).•The spin-liquid system Tb2Ti2O7 shows heavily suppressed thermal conductivity below 100 K.•The anomalous thermal conductivity of Tb2Ti2O7 can be attributed to the presence of unusually strong coupling between the phonons and crystal field excitations.Thermal conductivity measurements have been performed from 2 to 330 K on single crystals of pyrochlore R2Ti2O7 (R=Gd, Tb, Dy, Ho, Er, Lu, and Y). The spin-liquid system Tb2Ti2O7 shows heavily suppressed thermal conductivity below 100 K, which can be attributed to the presence of unusually strong coupling between the phonons and crystal electric field excitations in this compound. For the other R2Ti2O7 compounds, the magnetic moment of the R ion does not appear to play important roles in thermal conductivity for the present temperature region.