Approximate controllability for semilinear abstract discrete-time systems is considered. Specifically, we consider the semilinear discrete-time system xk+1=Akxk+f(k,xk)+Bkuk, k∈ℕ0, where Ak are bounded linear operators acting on a Hilbert space X, Bk are X-valued bounded linear operators defined on a Hilbert space U, and f is a nonlinear function. Assuming appropriate conditions, we will show that the approximate controllability of the associated linear system xk+1=Akxk+Bkuk implies the approximate controllability of the semilinear system.