Let Hi(i=1,2,…,n) be unitary space. Let A be a linear operator on H=H1⊕H2⊕…⊕Hn with block matrix expression ([Aij]n×n,n≤dim Hi<∞). This paper presents a necessary and sufficient condition of the block numerical range of matrix A equal to its spectrum: a set of complex numbers λ1,λ2,…,λm,(m≤n) exist and Aii=μiI(i=1,2,…,n). Moreover, the set of all μi is equal to {λ1,λ2,…,λm}, and can be transformed into an upper triangular block matrix by some elementary row operations and the corresponding elementary column operations.