  For the N=2 Kazama-Suzuki(KS) model on CP^3, the lowest higher spin current
with spins (2, 5/2, 5/2,3) is obtained from the generalized GKO coset
construction. By computing the operator product expansion of this current and
itself, the next higher spin current with spins (3, 7/2, 7/2, 4) is also
derived. This is a realization of the N=2 W_{N+1} algebra with N=3 in the
supersymmetric WZW model. By incorporating the self-coupling constant of lowest
higher spin current which is known for the general (N,k), we present the
complete nonlinear operator product expansion of the lowest higher spin current
with spins (2, 5/2, 5/2, 3) in the N=2 KS model on CP^N space. This should
coincide with the asymptotic symmetry of the higher spin AdS_3 supergravity at
the quantum level. The large (N,k) 't Hooft limit and the corresponding
classical nonlinear algebra are also discussed.
