Direction sensitivity could provide robust evidence for the direct detection of weakly interacting massive particles constituting dark matter. However, the sensitivity of this method remains low due to the radioactive backgrounds. The purpose of this study is to develop a low-background detector as a two-dimensional imaging device for a gaseous time projection chamber. In direction-sensitive dark matter experiments~(e.g. NEWAGE), $alpha$-rays emitted from the detector components often create substantial radioactive backgrounds. Based on the study of the background of NEWAGE, a new detector low-$alpha$ $mu$-PIC is developed. The produced $mu$-PIC performs well as a gas detector and the $alpha$-ray emission rate from the $mu$-PIC reduced by a factor of 100.