We consider a type of shrinking target problem in a conformal iterated function system.Let be a countable index set and Φ ={φ i:i ∈ ∧} be a conformal iterated function system on [0,1]d satisfying the open set condition.Denote by J the attractor of Φ.Define a set as {x ∈ J:|x-(φ w1...oφwn)-1(x)| ＜ e-Snf(x),wi ∈ ∧,1≤ i ≤ n,i.o.n ∈ N},where f:[0,1]d → R+ is a positive function,Snf(x) denotes f(x)+f( φ1w1(x))+...+ f((φ w1 o...o φ wn-1)-1(x)),analogous to the ergodic sum,and i.o.denotes infinitely often for brevity.The set defined above is analogous to the shrinking target one in a dynamical system.