The two-dimensional equilibrium with flexible boundaries is solved via using a MAT-LAB Equilibrium Code (MEC), which has applied the finite element method to handle the changeable plasma shape and employed the trust-region dogleg method to solve the nonlinear partial differential equation. The corresponding driven current profile is also calculated by coupling with the lower-hybrid simulation code (LSC). The results are applied to optimize the lower hybrid current drive (LHCD) efficiency for the Experimental Advanced Superconductor Tokamak (EAST) and suggested that both elongation and triangularity have a notable effect on the efficiency because of the competition between the increase in the resonant area and in the Shafranov shift. Moreover, large aspect-ratio has a negative effect on the efficiency. These effects are studied numerically, which might be considered carefully for both good plasma confinement and high LHCD efficiency.