There is a ~3 sigma discrepancy in the muon anomalous magnetic moment (g-2) between the measured value at BNL E821[1] and the Standard Model (SM) prediction. In order to cast light on beyond the SM, further investigations are necessary. The E34 experiment at J-PARC[2] aims to measure the muon g-2 with a precision of 0.1 ppm by utilizing newly developed novel technique of the low emittance muon beam. One of the key components to achieve the low emittance muon beam is the muon linear accelerator (linac)[3] which will be first case in the world. In addition, the substantial emittance growth during the acceleration should be prevented to satisfy the experimental requirements.
In this talk, the muon linac design[4] and current status will be presented after short introduction to the muon g-2 experiment and linac.

References:
[1] G.W. Bennett et al., Phys. Rev. D73, 072003, 2006.
[2] J-PARC E34 conceptual design report, 2011.
[3] M. Otani et al., PASJ2015 Proc. (Tsuruga, Japan, 2015) WEOM02.
[4] M. Otani et al., Phys. Rev. Accel. and Beams, 19, 040101, 2016.