An experimental and numerical study were made on the time-varying heat transfer coefficient h(t) between a tube-shaped casting and metal molds. One dimensional treatment was adopted in analyzing the heat flows between the casting and the inner and the outer mold. The sequential function specification method was employed to solve the nonlinear inverse heal conduction problem. In order to investigate the different behavior of h(t) for different alloys, casting experiments were carried out with three Al-base alloys and pure Al having different types of solidification behavior. It was found that the temperature change of the outer mold showed a normal heating and cooling curve. However, that of the inner mold was unusual especially for the alloys with a wide solidification range, i.e. the temperature increases first rapidly, then hails for a while and then increases again showing finally a regular heating and cooing curve. The resulting heat transfer coefficient at the interface to the inner mold h(i)(r) decreases temporarily and then increases, while the one al the interface to the outer mold h(o)(t) decreases monotonously to a quasi steady state. The abnormal heat transfer phenomenon at the inner interface for the alloys with a wide solidification range was concluded to be caused by a slight movement of the semi-solid inner wall at the inside of the tube-shaped casting due to the solidification contraction bf the casting freezing in a mushy type.