This paper first makes an attempt to investigate the partial information nearoptimal control of systems governed by forward-backward stochastic differentialequations with observation noise under the assumption of a convex controldomain. By Ekeland's variational principle and some basic estimates for stateprocesses and adjoint processes, we establish the necessary conditions for any$arepsilon $-near optimal control in a local form with an error order ofexact $arepsilon ^{% rac{1}{2}}.$ Moreover, under additional convexityconditions on Hamiltonian function, we prove that an $arepsilon $-maximumcondition in terms of the Hamiltonian in the integral form is sufficient fornear-optimality.
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