Abstract: With persistently increased data and bandwidth of signal, compressive sensing as a new low rate sampling method rapidly becomes a hotspot in signal processing society. Recently, compressive sensing usually measures the signal by linear manner. Chaotic Compressive Sensing (ChaCS) is a nonlinear compressive sensing theory which uses chaos systems to measure signals and performs the signal reconstruction by nonlinearly constrained L1-norm minimization. ChaCS is simple in implementation and generates secure measurement data. However, existing algorithms cannot efficiently solve the nonlinearly constrained L1-norm minimization, and the reconstruction quality is affected by the extra algorithm parameters. By linearization of nonlinear constraints, this paper proposes to solve the problem by iterative second order cone programming through the transformation of the nonlinearly constrained L1-norm minimization into a series of second order cone programming. The resulting algorithm is convergent and improves the reconstruction performance of signals. The Henon system is taken as examples to expose the estimation performance of frequency sparse signals. Numerical simulations illustrate the effectiveness of the proposed method.