The stoichiometric 111 iron-based superconductor, LiFeAs, has attacted great research interest in recent years. For the first time, we have successfully grown LiFeAs thin film by molecular beam epitaxy (MBE) on 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. Uniform LiFeAs film as thin as 3 quintuple-layer (QL) is formed. 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 coherence peaks is about 7 meV, close to the value of bulk material. The ex situ transport measurement of thick LiFeAs film shows a sharp superconducting transition around 16 K. The upper critical field, Hc2(0)=13.0 T, is estimated from the temperature dependent magnetoresistance. The precise thickness and quality control of LiFeAs film paves the road of growing similar ultrathin iron arsenide films.