The objective of this paper is to introduce a new class of submanifolds which are called pointwise quasi hemi-slant submanifolds in almost Hermitian manifolds which extends quasi hemi-slant, hemi-slant, semi-slant and slant submanifolds in a very natural way. Several basic results in this respect are proved in this paper. Moreover, we obtain some conditions of the distributions which are involved in the definition of the new submanifolds. We also get some results for totally geodesic and mixed totally geodesic conditions for pointwise quasi hemi-slant submanifolds. Finally, we illustrate some examples in order to guaranty the new kind of submanifolds.