In this paper, a Local Linear Radial Basis Function Neural Network (LLRBFN) is proposed. In this way the connection weights between the hidden layer units and output units of the RBFN are replaced by a local linear model. In comparison of LLRBFN and RBFN, the LLRBFN requires less number of neurons than the RBFN to approximate the same nonlinear system thus the LLRBFN is more efficient because the ability of approximation has been increasedbyplacingalocallinearmodelinsteadofthehidden layerunits