By using the spin-wave theory, an anisotropic ferrimagnetic spin chain was studied and its low-lying excitation energy spectrum was obtained.The thermodynamic quantities of the system, such as the free energy, specific heat etc.were calculated.The state of the system in an external magnetic field was considered and the strength of magnetization was investigated.In the presence of external magnetic field, there exists a magnetization plateau of the anisotropic ferrimagnetic spin chain.The plateau disappears with the increase of the anisotropic factor.By studying the physical properties of the system, it concludes that the anisotropic factor plays an important role in the anisotropic ferrimagnetic spin chain.It can restrain the quasi-particle excitation in the system when the value of the anisotropic factor is within two critical points.In other cases, this action will disappear.So, for the ferrimagnetic spin chain, the anisotropic factor plays like a switch.