Abstract: In this paper, we study a two-type linear fractional branching process with immigration. For n ≥ 0, let Z_n = (Z_{n, 1}, Z_{n, 2})^⊤ denote the population size of the nth generation excluding immigrants arriving at time n. We call time n a regeneration epoch if Z_n = 0. In the critical case, we derive the limiting distribution of regeneration counts up to time n.