Streamer is a strong ionizing region which advances very quickly in gases, liquids and solids. Streamer is a low-temperature plasma, which produces a variety of chemically reactive substances efficiently. So, streamer discharge has been widely adopted in industry. Furthermore, streamer is the initial stage of electric breakdown in long air gap. Studying the streamer discharge characteristics and its mechanism is the basis of external insulation in power transmission systems.Streamer branching is a significant characteristic during its development. Lichtenberg figure is the first clear recording of the filamentary structure of streamers. One of acceptable explanations is that the random fluctuations of the electron density ahead of streamer trigger branching. Furthermore, photoionization provides the necessary free electrons for the development of positive streamers. The experimental results show that the branching characteristics are closely related to the photoionization rate in streamer head. The streamer shows higher possibility of branching if the photoionization rate decreases. Since previous experiment is indirect evidence of this deduction, we turn to numerical models to study the influence of photoionization rates on positive streamer branching in atmospheric air. A three-dimensional particle-in-cell model with Monte Carlo collision (PIC-MCC) scheme called Pamdi3D (Teunissen J, Ebert U 2016 Plasma Sources Sci. Technol. 25 044005) is employed in this paper. The development and branching of positive streamersin a millimeter-scale needle-plane gap are simulated at atmospheric pressure. Different streamer branching behaviors are investigated by artificially changing the nitrogen-oxygen ratio, the absorption cross section of oxygen, and the photoionization efficiency coefficient.The effects of different photoionization parameters are systematically studied. When the nitrogen-oxygen ratio, photon absorption cross section or photoionization efficiency coefficient are reduced, the streamer branching occurs earlier in three cases after reducing the photoionization rate. These results imply that the streamer shows higher possibility of branching if the photoionization rate decreases. When the streamer propagates in a non-uniform electric field region and the photoionization rate decreases to a certain value, it is believed that the seed electron distribution is more susceptible to random fluctuations. It will lead to instability in the space charge layer of streamer, thus causing the streamer to branch. Hence it is proposed that streamer branch will be triggered more easily if the photoionization rate in the streamer head decreases, in the case without considering other seed electron sources.