Inside-fuel-injector flow conditions, such as injection pressure and gas-liquid two-phase cavitation flow dynamics, greatly affect fuel spray development and spray combustion performance of liquid-fuelled engine. The topic has attracted great interest for a long time. Measurement, however, has proven difficult due to harsh testing conditions on high pressure and flow velocity. On the other hand, computational approaches, which may play an important role in providing a detailed picture of inside-injector flow physics, are also limited due to the complexity of the needle movement and cavitating gas-liquid two-phase flow in the methodological framework of Navier-Stokes equations. Over the past three decades, the mesoscopic lattice Boltzmann method (LBM) has attracted great attention due to its simple scheme, easement of dealing with complex geometry and convenience of parallel computing. Its mesoscopic nature makes it greatly suitable for simulating multiphase and multispecies flow. LBM can also effectively collaborate with the immersed boundary method, since both approaches are usually discretised on regular Cartesian mesh, to deal with moving geometries in the computational domain. The clear advantages of the LBM over conventional approaches have motivated us to develop the approach for its applications in inner-injector flow, and a first-stage study is reported in this paper. First, an oscillating cylinder which moves in a sine function algorithm is simulated to model needle movement and validated by using the immersed boundary method. Second, the Shan-Chen multiphase flow model [14-16] is employed to model both a spinodal decomposition case and an inside-nozzle flow in which cavitation emerges behind the throating region of the model nozzle. It has been shown that both the immersed boundary method and the Shan-Chen model produce satisfactory results. Following the first-stage validation, we aim to further develop the LBM in collaboration with the immersed boundary method and Shan-Chen model to investigate flow dynamics inside a fuel injector where multiphase flow interacts with moving geometry.