ABSTRACT Recently , many dark energy models whose equation-of-state parameter can cross the phantom divide w _ { de } = -1 have been proposed . In a previous paper [ Class . Quant . Grav . 22 , 3189 ( 2005 ) ; hep-th/0501160 ] , we suggest such a model named hessence , in which a non-canonical complex scalar field plays the role of dark energy . In this work , the cosmological evolution of the hessence dark energy is investigated . We consider two cases : one is the hessnece field with an exponential potential , and the other is with a ( inverse ) power law potential . We separately investigate the dynamical system with four different interaction forms between hessence and background perfect fluid . It is found that the big rip never appears in the hessence model , even in the most general case , beyond particular potentials and interaction forms .