  We study the volume growth of hyperkaehler manifolds of type $A_{\infty}$
constructed by Anderson-Kronheimer-LeBrun and Goto. These are noncompact
complete 4-dimensional hyperkaehler manifolds of infinite topological type.
These manifolds have the same topology but the hyperkaehler metrics are depends
on the choice of parameters. By taking a certain parameter, we show that there
exists a hyperkaehler manifold of type $A_{\infty}$ whose volume growth is r^a
for each 3<a<4.
