Abstract: Research on the temporal relaxation of plasmas is of significance in the applications of low temperature plasma. In order to study the temporal relaxation of plasmas with different densities under the action of crossed electric and magnetic fields, electron relaxation properties were calculated based on multi-term approximation of the Boltzmann equation. Firstly electron relaxation properties of Reid model gas with different densities were calculated. It is shown that: 1) bulk drift velocity WBx in the x-axis direction, bulk drift velocity WBzin the z-axis direction, diffusion coefficients Dii exhibit damped periodic decay as the time t increases, while relaxation of electron mean energy ε is monotonic; 2) there is three distinct timescales: the electron gyration period γ g, the momentum relaxation time γ m and the energy relaxation time γ e. And the timescales satisfy γ g ＜ γ m ＜ γ e; 3) bulk drift velocity WBx, bulk drift velocity WBz, electron mean energy ε, combination parameter n0 Dii of plasmas with different densities as a function of dimensionless time n0 t all show similarity laws. In the end the similarity laws of electron relaxation was explained from dimensionless approach and physical meaning. From the perspective of dimensionless approach, bulk drift velocity WBi, electron mean energy ε, combination parameter n0 t and n0 Diiare all invariants or combination invariants. From the perspective of physical meaning, collision frequency ν is proportional to gas density n0, so combination parameter n0 t is a dimensionless time, bulk drift velocity WBi is proportional to reduced electric field E/n0, electron mean energy ε only relates to reduced electric and magnetic field, diffusion coefficients Diiis inversely proportional to gas density n0.