The temperature dependence of the anisotropy parameter of upper critical field γHc2 (T) Hc2 (T)/Hc2 (T) and London penetration depth γλ(T) λ(T)/λ (T) are calculated using two-band Ginzburg-Landau theory for layered superconductors. It is shown that, with decreasing temperature the anisotropy parameter γHc2 (T) is increased, while the London penetration depth anisotropy γλ(T) reveals an opposite behavior. Results of our calculations are in agreement with experimental data for single crystal MgB2 and with other calculations. Results of an analysis of magnetic field Hc1 in a single vortex between superconducting layers are also presented.