We study in this article the Pontryagin's maximum principle for a class of control problems associated with the primitive equations (PEs) of the ocean with two point boundary state constraint. These optimal problems involve a two point boundary state constraint similar to that considered in Wang, Nonlinear Anal. 51, 509-536, 2002 for the three-dimensional Navier-Stokes (NS) equations. The main difference between this work and Wang, Nonlinear Anal. 51, 509-536, 2002 is that the nonlinearity in the PEs is stronger than in the three-dimensional NS systems.