The collision frequencies of electron-neutral-particle in weakly ionized complex plasmas with the non-Maxwellian velocity distributions are studied.The average collision frequencies of electron-neutral-particle in plasmas are accurately derived.We find that these collision frequencies are significantly dependent on the power-law spectral indices of non-Maxwellian distribution functions and so they are generally different from the collision frequencies in plasmas with a Maxwellian velocity distribution,which will affect the transport properties of the charged particles in plasmas.Numerically analyses are made to show the roles of the spectral indices in the average collision frequencies respectively.