The stoichiometric “111” iron-based superconductor, LiFeAs, has attacted great research interest in recent years. For the first time, we have successfully grown a LiFeAs thin film by molecular beam epitaxy (MBE) on a SrTiO3(001) substrate, and studied the interfacial growth behavior by reflection high-energy electron diffraction (RHEED) and low-temperature scanning tunneling microscope (LT-STM). The effects of substrate temperature and Li/Fe flux ratio were investigated. A uniform LiFeAs film as thin as 3 quintuple layers (QL) is formed. A superconducting gap appears in LiFeAs films thicker than 4 QL at 4.7 K. When the film is thicker than 13 QL, the superconducting gap determined by the distance between the coherence peaks is about 7 meV, close to the value of bulk material. The ex situ transport measurement of a thick LiFeAs film shows a sharp superconducting transition around 16 K. The upper critical field, , is estimated from the temperature-dependent magnetoresistance. The precise thickness and quality control of the LiFeAs film paves the road for growing similar ultrathin iron arsenide films.