Ultraviolet (UV) and vacuum-UV pulses (VUV) were simultaneously generated by using four-wave mixing through filamentation in neon gas. Second harmonic of Ti:sapphire laser output (400 nm, omega(SHG)) and near infrared pulses (1200 nm, omega(NIR)) from a noncollinear optical parametric amplifier were gently focused into neon gas, and ultrashort pulses with the center wavelengths of 237 nm (omega(fwm)) and 167 nm (omega(cas)) were produced by four-wave mixing processes omega(SHG) + omega(SHG) - omega(NIR) --> omega(fwm) and omega(fwm) + omega(SHG) - omega(NIR) --> omega(cas), respectively. The energy of the generated 237 nm pulse was more than one micro joule. Transfer of spectral phase from the near infrared ultrashort pulses to the UV pulses through the four-wave mixing process was also demonstrated. The even order spectral phase of the near infrared pulse was transfered to the UV pulse with the opposite sign, whereas the odd order spectral phase was transfered with the same sign. A positively chirped near infrared pulse was used for generating a negatively chirped UV pulse, which was compressed down to 25 fs by a magnesium fluoride window. In principle, the spectral phase transfer scheme can also be applied to the chirp control of the generated VUV pulses.