  Inspired by the $f(R)$ non-linear massive gravity, we propose a new kind of
modified gravity model, namely $f(T)$ non-linear massive gravity, by adding the
dRGT mass term reformulated in the vierbein formalism, to the $f(T)$ theory. We
then investigate the cosmological evolution of $f(T)$ massive gravity, and
constrain it by using the latest observational data. We find that it slightly
favors a crossing of the phantom divide line from the quintessence-like phase
($w_{de} > -1$) to the phantom-like one ($w_{de} < -1$) as redshift decreases.
