Single-image　super-resolution　(SISR)　techniques　have　been　developed　rapidly　with　the　remarkable　progress　of　convolutional　neural　networks　(CNNs).　The　previous　CNNs-based　SISR　techniques　mainly　focus　on　the　network　design　while　ignoring　the　interactions　and　interdependencies　between　different　dimensions　of　the　features　in　the　middle　layers,　consequently　hindering　the　powerful　learning　ability　of　CNNs.　In　order　to　address　this　problem　effectively,　a　residual　triplet　attention　network　(RTAN)　for　efficient　interactions　of　the　feature　information　is　proposed.　Specifically,　we　develop　an　innovative　multiple-nested　residual　group　(MNRG)　structure　to　improve　the　learning　ability　for　extracting　the　high-frequency　information　and　train　a　deeper　and　more　stable　network.　Furthermore,　we　present　a　novel　lightweight　residual　triplet　attention　module　(RTAM)　to　obtain　the　cross-dimensional　attention　weights　of　the　features.　The　RTAM　combines　two　cross-dimensional　interaction　blocks　(CDIBs)　and　one　spatial　attention　block　(SAB)　base　on　the　residual　module.　Therefore,　the　RTAM　is　not　only　capable　of　capturing　the　cross-dimensional　interactions　and　interdependencies　of　the　features,　but　also　utilizing　the　spatial　information　of　the　features.　The　simulation　results　and　analysis　show　the　superiority　of　the　proposed　RTAN　over　the　state-of-the-art　SISR　networks　in　terms　of　both　evaluation　metrics　and　visual　results.