A multi-type preferential attachment tree is introduced, and studied using general multi-type branching processes. For the p-type case we derive a framework for studying the tree where a type i vertex generates new type j vertices with rate wij(n1,n2,…,np) where nk is the number of type k vertices previously generated by the type i vertex, and wij is a non-negative function from Np to R. The framework is then used to derive results for trees with more specific attachment rates. In the case with linear preferential attachment—where type i vertices generate new type j vertices with rate wij(n1,n2,…,np)=γij(n1+n2+⋯+np)+βij, where γij and βij are positive constants—we show that under mild regularity conditions on the parameters {γij},{βij} the asymptotic degree distribution of a vertex is a power law distribution. The asymptotic composition of the vertex population is also studied.