In this study, we define the notion of conformal semi-slant Riemannian maps from almost Hermitian manifolds onto Riemannian manifolds as a generalization of conformal semi-slant submersions. We give examples for this type maps. We study integrability conditions of distributions. In addition, we apply pluriharmonic maps to investigate being horizontally homothetic map. Moreover, we examine that under which cases, the distributions can define totally geodesic foliations.