A quantum transport theory is developed for ferromagnetic semiconductor nanostructures, where a ferromagnetic central region (FCR) is coupled to non-magnetic leads. The strong spin-spin interaction between the charge carriers and the localized magnetic electrons causes a large splitting of the energy levels between the spin-up and spin-down carriers and increases strongly the charge carrier scattering rate due to the spin disorder scattering in the FCR. The electronic structure of the FCR and the scattering rate can be estimated from the real and imaginary parts of the poles of the retarded Green's function including the spin-spin interaction. Then a quantum transport theory can be developed by using the Keldysh non-equilibrium-Green-function technique. A general expression for the transmission coefficient T(E) can be calculated by using the retarded and advanced Green functions for the FCR. Numerical results are presented for a ferromagnetic AlAs/(Ga,Mn)As/AlAs quantum well with a single resonant level coupled to the non-magnetic metallic leads by tunneling. The calculated results show that the strong spin-spin interaction leads to a shift and a broadening of the peak for T(E) as compared to the non-interacting case. Also a double peak structure due to the splitting of the resonant level is shown in the ferromagnetic temperature region.