It is known that there exist no warped product semi-slant submanifolds in Kahler manifolds . Recently, Chen and Garay studied pointwise slant submanifolds of almost Hermitian manifolds in  and obtained many new results for such submanifolds. In this paper, we first introduce pointwise semi-slant submanifolds of Kahler manifolds and then we show that there exists non-trivial warped product pointwise semi-slant submanifolds of Kahler manifold by giving an example, contrary to the semi-slant case. We present a characterization theorem and establish an inequality for the squared norm of the second fundamental form in terms of the warping function for such warped product submanifolds in Kahler manifolds. The equality case is also considered.