Proposes a generalized collaboration network which the number of collaborators T is a random variable, the new member with probability p chooses T-1 collaborators randomly and with probability 1-p chooses T-1 collaborators preferentially. Through node degree changing, meets Markov property, and by means of Markov chain theory obtains accurate analytic expression of degree distribution. The value of the parameter p determines the scale-free property of this generalized collaboration network, and when p<1, the network is scale-free and the scale exponent is a function of p.