We study the collision frequencies of particles in the weakly and highly ionized plasmas with the power-law q-distributions in nonextensive statistics. We derive the average collision frequencies of neutral–neutral particle, electron–neutral particle, ion–neutral particle, electron–electron, ion–ion and electron–ion, respectively, in the q-distributed plasmas. We show that the average collision frequencies depend strongly on the q-parameter in a complex form and thus their properties are significantly different from those in Maxwell-distributed plasmas. These new average collision frequencies are important for us to study accurately the transport property in the complex plasmas with non-Maxwell/power-law velocity distributions.