Two-dimensional surface structures often host a surface state in the bulk gap, which plays a crucial role in the surface electron transport. The diversity of in-gap surface states extends the category of two-dimensional systems and gives us more choices in material applications. In this article, we investigated the surface states of β-√3 × √3-Bi/Si(111) surface by scanning tunneling microscopy. Two nearly free electron states in the bulk gap of silicon were found in the unoccupied states. Combined with first-principles calculations, these two states were verified to be the Bi-contributed surface states and electron-accumulation-induced quantum well states. Due to the spin-orbit coupling of Bi atoms, Bi-contributed surface states exhibit free-electron Rashba splitting. The in-gap surface states with spin splitting can possibly be used for spin polarized electronics applications.