let $g$ be an automorphism group of a‎ ‎$2$-$(v,k,4)$ symmetric design $mathcal d$‎. ‎in this paper‎, ‎we‎ ‎prove that if $g$ is flag-transitive point-primitive‎, ‎then the‎ ‎socle of $g$ cannot be an exceptional group of lie type‎.