The electron energy distribution function (EEDF) of weakly ionized air plasma (79% nitrogen and 21% oxygen) is investigated by solving the Boltzmann equation with the spherical harmonics expansion. It is found that the EEDF deceases sharply in an energy range from 2 to 3 eV for low reduced field (E/N 100 Td), and the high energy tail of the EEDF decreases more sharply than Maxwell distribution. When the reduced field increases to a range 400 to 2000 Td, the EEDF approaches to Maxwell distribution. When the reduced field is greater than 2000 Td, the high energy tail (200 eV) of the EEDF deceases more slowly than Maxwell distribution. It is shown that the EEDF approaches to Maxwell distribution in a high frequency field. The effective electron temperature is dependent only on E/ for vm, but on E/N for vm. The electron-electron collisions play no significant role until the ionization degree is bigger than 0.1%. This is different from the case of monatomic plasmas, in which the EEDF is influenced by electron-electron collisions for ionization degree greater than 10-6.