In this paper, we propose a novel algorithm, "Power- ICA", for independent component analysis (ICA) that is analog of the power iteration for solving the eigenvalue problem of a matrix. In each iteration the updating of ICA matrix is fully-multiplicative, rather than the partly multiplicative and partly additive in the conventional learning algorithms. Therefore, this algorithm presents a new class of algorithm to the ICA algorithms. The cost function for algorithm is based on a diagonality of a non-linearized covariance matrix. One of desired features is that the algorithm does not include any pre-designated parameter such as the learning step size, which is promising for applications to ICA with unknown types of sources. We also give conditions for choices of the non-linear functions. Numerical results show the effectiveness of PowerICA.