  We study intersecting D-branes in a type IIB plane wave background using
Green-Schwarz worldsheet formulation. We consider all possible $D_\pm$-branes
intersecting at angles in the plane wave background and identify their residual
supersymmetries. We find, in particular, that $D_\mp - D_\pm$ brane
intersections preserve no supersymmetry. We also present the explicit
worldsheet expressions of conserved supercharges and their supersymmetry
algebras.
