Summary: The article is devoted to the problem of holomorphically projective transformations of locally conformal Kähler manifolds. J. Mikes and Z. Radulovich proved that a locally conformal Kähler manifold does not admit finite nontrivial holomorphically projective mappings for a Levi-Civita connection. Earlier we also shown that a locally conformal Kähler manifold also does not admit nontrivial infinitesimal holomorphically projective transformations for a Levi-Civita connection. But since the Weyl connection defined by Lee form on a locally conformal Kähler manifold is \(F\)-connection, hence for the connection nontrivial infinitesimal holomorphically projective transformations are admitted. Then we rewrote the system of partial differential equations for the Levi-Civita connection. So we introduced so called infinitesimal conformal holomorphically projective transformations. We have got the necessary and sufficient conditions in order that the a locally conformal Kähler manifold admits a group of infinitesimal conformal holomorphically projective transformations. Also we have calculated the number of parameters which the group depend on. We have got invariants, i.e. a tensor and a non-tensor which are preserved by the transformations. And finally, we have proved that a vector field which generates infinitesimal conformal holomorphically projective transformations of a compact locally conformal Kähler manifold is contravariant almost analytic.