In this paper the Friedmann-Robertson-Walker model with a traversable wormhole is considered. It is shown that total matter including cosmic and wormhole matter cannot be exotic, while matter is exotic in the static and inflating wormhole spacetimes. This implies that it is not necessary for total matter to violate the energy conditions in the cosmological model with a traversable wormhole. Assume that the matter is divided into two parts: the cosmic part that depends on time only and the wormhole part that depends on space only. The time development and the spatial dependences of the scale factor, matter, and the wormhole shape function are also obtained.