The oscillations of a class of vector parabolic partial differential equations with continuous distribution arguments are studied. By employing the concept of H-oscillation and the method of reducing dimension with inner product, the multi-dimensional oscillation problems are changed into the problems of which one-dimensional functional differential inequalities have not eventually positive solution. Some new sufficient conditions for the H-oscillation of all solutions of the equations are obtained under Dirichlet boundary condition,where H is a unit vector of RM.