Faintly continuous (FC) functions, entitled faintly 𝜃S-continuous and faintly δS-continuous functions have been introduced and investigated via a 𝜃-open and 𝛿-open sets. Several characterizations and properties of faintly 𝜃S-continuous and faintly 𝛿𝑠-Continuous functions were obtained. In addition, relationships between faintly 𝜃s- Continuous and faintly 𝛿S-continuous function and other forms of FC function were investigated. Also, it is shown that every faintly 𝜃 S-continuous is weakly 𝜃S-continuous. The Convers is shown to be satisfied only if the co-domain of the function is almost regular.