Abstract: To construct the novel fractals, we present a method which can be used to construct a nonlinear IFS composed of the complex quadratic polynomials with single complex parameter. First, we construct the 1-period parameter set in the parameter plane; then, randomly choose more than 2 parameters in the set and build a set of the contract functions; next, build a nonlinear IFS with these functions; last, continuously iterate the fixed point of a contract function by randomly choosing a function in the IFS to construct a fractal or a strange attractor. The result shows that the method to construct the nonlinear IFS presenting in this paper is valid to construct the strange attractors or fractals in the plane, which have the new structures differing from the fractals coming from the linear IFS.