Developing shape memory polymers (SMPs) with enough mechanical strength, good toughness and excellent processability(mild synthesis conditions) is still a challenge for researchers. Therefore, a series of rigid-flexible epoxy SMPs were prepared based on epoxy resin, trimethylolpropane tris(3-mercaptopropionate) (TMP), and N,N-diglycidyl-4-glycidyloxyaniline (TGE) through thiol-epoxy click-reaction. The effect of sulfide curing agent and modifier on the crosslink networks and main features (mechanical strength, toughness, and shape memory performance) of epoxy samples were investigated. Experimental results displayed temperature-dependent modulus and strength with two order of magnitude difference between room temperature and glass transition temperature (Tg). TGE showed great effect on the improvement of mechanical properties of the epoxy material, increasing from 724.2 MPa to 1637 MPa, nearly 220%. Moreover, shape-memory test revealed that prepared epoxy SMPs are capable to fulfil the recovery process within 2 mins as long as temperature elevated to or above Tg, with shape fixity ratio over 99 % and shape recovery ratio above 90 %.