This study proposes a reduced-dimension identification algorithm for systems with unknown structures. By using the kernel method, the unknown structure systems are approximated by a Volterra model with a high-dimension. To avoid high-order matrix inverse and eigenvalue calculations, a variable elimination algorithm is developed, which decomposes the high-dimension model into two sub-models. The theoretical analysis shows that the variable elimination algorithm has a faster convergence rate than that of the traditional gradient descent algorithm. In addition, an Aitken method is introduced to increase the convergence rates and to make the algorithm be robust to the step-size. The simulation results verify the effectiveness of the algorithm.