In this paper, we propose a new method which makes transient simulation faster for the circuit including both nonlinear and linear elements. First, the method for generating the projection matrix with Krylov-subspace technique is described. The order of the circuit equation is reduced by congruence transformation with the projection matrix. Next, we suggest a method which can calculate the reduced Jacobian matrix directly in the each Newton-Raphson iteration. Since this technique does not need to calculate the original size of Jacobian matrix, the calculation cost is reduced drastically. Therefore, efficient circuit simulation can be achieved. Finally, our method is applied to some example circuits and the validity of the nonlinear circuit reduction technique is verified.