The time development of the electron distribution function and electron macroscopic parameters was studied by solving the time-dependent Boltzmann equation for low temperature plasma. A new technique for solving the time-dependent Boltzmann equation was developed. This technique is based on a multi-term approximation of the electron distribution function expansion in Legendre polynomials. The results for electron relaxation in Reid's ramp model and argon plasma are presented. The effect of negative mobility was studied and is discussed for argon plasma. Finally, the time-dependent Boltzmann equation was solved for pulsed microwave discharge in nitrogen. The accuracy of all results was confirmed by the Monte Carlo simulation.