The propagation of picosecond deep ultraviolet laser pulse at wavelength of 193 nm in air is numerically investigated. Long plasma channel can be formed due to the competition between Kerr self-focusing and ionization induced defocusing. The plasma channel with electron density of above 10<sup>13</sup>/cm<sup>3</sup> can be formed over 70 m by 50-ps, 20-mJ laser pulses. The fluctuation of laser intensity and electron density inside ultraviolet (UV) plasma channel is significantly lower than that of infrared pulse. The linear absorption of UV laser by air is considered in the simulation and it is shown that the linear absorption is important for the limit of the length of plasma channel.