Streamer, which usually appears at the initial stage of atmospheric pressure air discharge, acts as a precursor of lightning. It also occurs as large discharges (called sprites) in upper atmosphere, far above the thundercloud. The streamer discharge has many potential applications in industry, such as gas or water cleaning, ozone generation, assisted combustion, etc. The streamer discharge is difficult to investigate both experimentally and computationally, because of its non-linear and multi-scale characteristics. Various studies on streamer discharge have been carried out, and some progress has been made. However, some things remain to be further understood, i.e., the law of particles motion and the factors influencing streamer discharge. In this paper, we use a pre-established three-dimensional (3D) particle model (PIC/MCC) to study streamer discharge with a needle-plate electrode in air. To simplify the condition, we only use nitrogen-oxygen mixture to represent dry air, regardless of other components such as CO2, H2O gases, etc. In this model, we take photoionization, attachment and detachment processes into account. The adaptive mesh refinement and adaptive particle weight techniques are used in the code. In order to facilitate the simulation, we artificially put a Gaussian seed right on the top of the needle electrode. We adjust some computational parameters to analyze how the streamer discharge starts and evolves from the needle electrode. Many factors can influence streamer discharge during its evolution, from among which we choose three important parameters:voltage amplitude, gas component, and the radius of curvature of the needle electrode tip, to study the generation and evolution of streamer discharge, and focus on inception cloud, streamer branches, and electric fields. The simulation results show that the radius of inception cloud increases with the increase of voltage amplitude, and the diameter of steamer channel and the number of branches also increase with voltage increasing. We choose 4 kV as a proper simulation voltage for next two parts of simulations. By comparing the results obtained in the cases of different gas components (pure oxygen and different ratios of nitrogen-oxygen mixtures), we discover that the nitrogen-oxygen mixture ratio significantly affects the total number of streamer branches. With 0.1% oxygen, discharge grows irregularly with small protrusions on streamers. In the pure oxygen case, streamer seems to have much more thin branches than in other cases. Needle geometry directly changes the inception cloud of the streamer and its morphology, especially when the tip becomes blunter. In this circumstance, electric field strength around the electrode decreases, and inception cloud can be barely seen. Instead, a single-channel streamer discharge develops right toward the plate electrode, later this single-channel streamer splits into branches.