A numerical simulation is carried out on the interaction between the magnetic cloud and the follow-up highspeed stream observed at 1 AU August 27 - 28,1978, and it basically reproduces the observed profiles. The numerical results show that the magnetic cloud - highspeed stream system leads to the formation of a forward fast and slow shock as well as a reverse fast shock. The forward fast and slow shocks originate from the magnetic cloud whereas the reverse fast shock is generated by the highspeed stream. However, the properties of these shocks have been affected by the interaction between the magnetic cloud and the high speed stream in various degrees. Under the pursuit of the highspeed stream, the magnetic cloud is restrained from expansion at its tail part, where a structure of high temperature, high density and strong magnetic field is formed.