The authors Selvi.R, Thangavelu.P and Anitha.m introduced the concept of continuity between a topological space and a non empty set where {L, M, R, S} [4]. Navpreet singh Noorie and Rajni Bala[3] introduced the concept of f# function to characterize the closed, open and continuous functions. In this paper, the concept of Semi ρ continuity is introduced and its properties are investigated and Semi ρ continuity is further characterized by using f# functions.