To provide a sound aluminum single crystal or unidirectional solidified cast body having little porosity on the surface layer by preventing gas absorption in the solidified part at the casting time, and to provide a producing method thereof.

In a continuous casting method of the aluminum alloy single crystal or unidirectional solidified body solidify-cast to the unidirection by adding the additional elements of one or more kinds among the elements of the atomic number 3 to 83 except the rare gas into the single crystal or the unidirectional solidified body of aluminum having ≥99.9 wt.% purity or the aluminum having ≥99.9 wt.% purity, a gap between the inner surface of a mold and the solidified cast body at the outlet side part of the mold for continuous casting is replaced with a dry gas atmosphere having ≤-20°C dew point. The continuously cast material of the high purity aluminum is produced with the above method. An aluminum alloy single crystal target is obtd. by using the continuously cast material of the high purity aluminum with the above- manner.