Straightplasma channels are widely used to guide relativistic intense laser pulses over several Rayleigh lengths for laser wakefield acceleration. Recently, a curved plasma channel with gradually varied curvature was suggested to guide a fresh intense laser pulse and merge it into a straight channel for staged wakefield acceleration [Phys. Rev. Lett. 120, 154801 (2018)]. In this work, we report the generation of such a curved plasma channel from a discharged capillary. Both longitudinal and transverse density distributions of the plasma inside the channel were diagnosed by analyzing the discharging spectroscopy. Effects of the gas-filling mode, back pressure and discharging voltage on the plasma density distribution inside the specially designed capillary are studied. Experiments show that a longitudinally uniform and transversely parabolic plasma channel with a maximum channel depth of 47.5 μm and length of 3 cm can be produced, which is temporally stable enough for laser guiding. Using such a plasma channel, a laser pulse with duration of 30 fs has been successfully guided along the channel with the propagation direction bent by 10.4°.