  The affine quantum Schur algebra is a certain important infinite dimensional
algebra whose representation theory is closely related to that of quantum
affine $\frak{gl}_n$. Finite dimensional irreducible modules for the affine
quantum Schur algebra ${\mathcal S}_{\vartriangle}(n,r)_{v}$ were classified in
\cite{DDF}, where $v\in{\mathbb C}^*$ is not a root of unity. We will classify
blocks of the affine quantum Schur algebra ${\mathcal
S}_{\vartriangle}(n,r)_{v}$ in this paper.
