Let G be a compact connected semisimple Lie group, B the Killing form of the algebra g of G, and g the invariant metric induced by B. Then, we obtain a necessary and sufficient condition for a left invariant linear connection D with a Weyl structure (D, g,

) on (G, g) to be projectively flat (resp. Einstein-Weyl). And, we also get that if a left invariant linear connection D with a Weyl structure (D, g,

) on (G, g) which has symmetric Ricci tensor

is projectively flat, then the connection D is Einstein-Weyl: but the converse is not true. Moreover, we show that if a left invariant connection D with Weyl structure (D, g,

) on (G, g) is projectively flat (resp. Einstein-Weyl), then D is a Yang-Mills connection.