Rashba effect is much related to next-generation spintronic devices. It is highly desirable to search for Rashba materials with large Rashba spin splitting, which is considered as the key factor for the application of spin field-effect transistor. Here, we design a two-dimensional monolayer of fluorated-InTe (InTeF) with large Rashba spin splitting and direct bandgap on the basis of first-principles calculations. InTeF monolayer is energetically and dynamically stable based on the calculations of cohesive energy and phonon dispersion. Remarkably, the Rashba parameter alpha(R) is about 1.08 eV.angstrom, comparable to that of the BiTeI monolayer (1.86 eV.angstrom). The direct bandgap is estimated to be 2.48 eV by HSE06 hybrid functional, which shows good prospects in light-emitting devices and photodetectors. To further explore the effect of substrates on the electronic structure of InTeF monolayer, we build two heterostructures, and the results show that the strength of Rashba effect and the direct bandgap nature in InTeF monolayer can be well preserved under the influence of substrates. Based on the above findings in our work, InTeF monolayer is considered to be one of the promising 2D materials for the application of spintronics as well as optoelectronics.