Abstract: The elementary excitations spectrum in the system of a spin 1/2 one-dimensional ferrimagnetic diamond- like chain at low temperature is calculated by using the invariant eigen-operator method. The elementary excitations energy under especial qualification in the system and advantages or deficiencies of invariant eigen-operator method are discussed.

Key words: invariant eigen-operator method, unitary transformation, elementary excitations spectrum, a spin1/2 one-dimensional ferrimagnetic diamond-like chain