We present an analytical analysis of the actors’ degree distribution of collaboration networks by the rate equation approach. The results show that the actors’ degree follows a Yule-Simon distribution and this distribution can be well approximated by a shifted power law function. We find that the actors’ degree distribution has a large deviation from power-law with the increase of the growth speed of actors. It indicates that the growth speed of actors is another key factor influencing the topological properties of collaboration networks besides preferential attachment. The results of our analytical analysis can be well fitted with the empirical data from some public transport networks and scientists collaboration networks. Furthermore, we discuss the generating mechanism of the growth speed of actors in evolution of collaboration networks and its potential value of application in real-world networks.