We describe the edge states of fractional quantum Hall systems with alternating compressible and incompressible strips using a composite-fermion picture. The current carried by composite fermions in a compressible region depends on the difference between the electron filling factors in the two adjacent incompressible regions, consistent with the results of the interacting-electron picture given by Beenakker [Phys. Rev. Lett. 64, 216 (1990)] and tested by recent experiments. This result allows the application of the Landauer-Buttiker formula for the composite fermion transport. [S0031-9007(98)08210-6].