This study focuses on a discrete-time Hammerstein system to investigate the identification with quantised inputs and quantised output observations. After the discussion of the system identifiability and by parameterising the static non-linear function, a three-step algorithm is proposed to estimate the unknown parameters for the identifiable system. The strong convergence and the mean-square convergence rate of the algorithm are established. It is shown that the asymptotic efficiency can be achieved in terms of the Cramer-Rao lower bound by selecting a suitable transformation matrix. A numerical simulation is given to demonstrate the effectiveness of the algorithm.