Ab initio electronic structure calculations reveal that epitaxial strain has a dramatic effect on the voltage-controlled magnetic anisotropy (VCMA) in Ta/FeCo/MgO junctions. Strain can give rise to a wide range of novel VCMA behaviors where the MA can change from a ∨-to a ∧-shape electric-field dependence with giant VCMA coefficients which are asymmetric under voltage reversal. The underlying mechanism is the interplay of the strain-and electric-field-induced changes in the spin-orbit coupled d states at the interfaces and the strain-induced modification of the dielectric constant of MgO. These findings demonstrate the feasibility of highly sensitive VCMA through strain engineering, which may provide a viable avenue for tailoring magnetoelectric properties for spintronic applications.