Fixed-point algorithms are widely used for independent component analysis(ICA) owing to its good convergence. However, most existing complex fixed-point ICA algorithms are limited to the case of circular sources and result in phase ambiguity, that restrict the practical applications of ICA. To solve these problems, this paper proposes a two-stage fixed-point ICA(TS-FPICA) algorithm which considers complex signal model. In this algorithm, the complex signal model is converted into a new real signal model by utilizing the circular coefficients contained in the pseudo-covariance matrix. The algorithm is thus valid to noncircular sources. Moreover, the ICA problem under the new model is formulated as a constrained optimization problem, and the real fixed-point iteration is employed to solve it. In this way, the phase ambiguity resulted by the complex ICA is avoided. The computational complexity and convergence property of TS-FPICA are both analyzed theoretically. Simulation results show that the proposed algorithm has better separation performance and without phase ambiguity in separated signals compared with other algorithms. TS-FPICA convergences nearly fast as the other fixed-point algorithms, but far faster than the joint diagonalization method, e.g. joint approximate diagonalization of eigenmatrices(JADE). Fixed-point algorithms are widely used for independent component analysis (ICA) owing to its good convergence. However, most existing complex fixed-point ICA algorithms are limited to the case of circular sources and result in phase ambiguity, that restrict the practical applications of ICA. To solve these problems, this paper, proposes a two-stage fixed-point ICA (TS-FPICA) algorithm which considers complex signal model. In this algorithm, the complex signal model is converted into a new real signal model by utilizing the circular coefficients contained in the pseudo-covariance matrix. The, the ICA problem under the new model is formulated as a constrained optimization problem, and the real fixed-point iteration is employed to solve it. way, the phase ambiguity resulted by the complex ICA is avoided. The computational complexity and convergence property of TS-FPICA are both analyzed theoretically. Simulation results show th at the proposed algorithm has better separation performance and without phase ambiguity in separated signals compared with other algorithms. TS-FPICA convergences nearly fast as the other fixed-point algorithms, but far faster than the joint diagonalization method, eg joint approximate diagonalization of eigenmatrices JADE).