A graph Г is said to be 2Гconnected if Г does not have a cut vertex. The power graph P(G) of a group G is the graph which has the group elements as vertex set and two elements are adjacent if one is a power of the other. In an earlier paper, it is conjectured that there is no non-abelian _nite simple group with a 2Гconnected power graph. Bubboloni et al. [3] and independently Doostabadi and Farrokhi D. G. [11], presented counterexamples for this conjecture. The aim of this paper is to _rst modify this conjecture and then prove this modi_ed conjecture for the sporadic groups, Ree groups 2F4(q) and 2G2(q), the Chevalley groups A1(q);B2(q);C3(q) and F4(q), the unitary group U3(q), the symplectic group S4(q) and the projective special linear group PSL(3; q), where q is a prime power.