The aim of the present paper is to study the properties of Kenmotsu manifolds admitting a special projective semi-symmetric connection. We have discovered that if a Kenmotsu manifold of n dimension (n > 2), is Ricci flat with respect to special projective semi-symmetric connection whose 1-form ŋ is a recurrent, then the manifold is a certain class of quasi-η Einstein manifold. Finally, we show that Weyl projective curvature tensor with respect to special projective semi-symmetric connection is cyclic on the Kenmotsu manifold.