ABSTRACT Recently , Geng et al . proposed to allow a non-minimal coupling between quintessence and gravity in the framework of teleparallel gravity , motivated by the similar one in the framework of General Relativity ( GR ) . They found that this non-minimally coupled quintessence in the framework of teleparallel gravity has a richer structure , and named it “ teleparallel dark energy ” . In the present work , we note that there might be a deep and unknown connection between teleparallel dark energy and Elko spinor dark energy . Motivated by this observation and the previous results of Elko spinor dark energy , we try to study the dynamics of teleparallel dark energy . We find that there exist only some dark-energy-dominated de Sitter attractors . Unfortunately , no scaling attractor has been found , even when we allow the possible interaction between teleparallel dark energy and matter . However , we note that w at the critical points is in agreement with observations ( in particular , the fact that w = -1 independently of \xi is a great advantage ) .